Washing ones hands with salt/ soap/fats:
It is forbidden to wash ones hands in salt and certainly with soap or other fats.
The reason for this is: because [the material] dissolves in ones hand and is as if one has created a new substance on Shabbos which resembles a forbidden action, as was explained above in Halacha 1 that it is forbidden to crush snow and hail for this reason. [This prohibition is referred to as Molid.]
Other Opinions: [However] according to those which [held there] that the reason for the prohibition of crushing snow and hail is because of a decree made [to safeguard one from coming to] squeeze fruits which are designated
for their juices, and snow and hail are likewise designated for their liquids as was explained there [in 320/19], [then according to them] soap and other fat which are not designated as liquids are permitted to be [even] initially crushed.
The Final Ruling: One is to be stringent like the former opinion.
Summary of using soap:
Has the same status as ice [stated above in Halacha 1-3], and thus although may be placed in water to dissolve it may not be dissolved with ones hands. Nevertheless one may place salt in water and wash with it, so long as he does not rub his hands in the process.
Does washing ones hands with a bar of soap contain the smoothening prohibition [Mimacheik] and would thus be prohibited according to all?
Regarding the Mimacheik/smoothening prohibition some Poskim hold it applies to soft soap and thus using it would be forbidden according to all opinions. The Ketzos Hashulchan however, as well as other Poskim argue that there is no smoothening prohibition applicable in such a case for variety of reasons [see footnote].
In any event the custom is not to wash at all with a bar of soap, as explained above that we are stringent like the opinion which holds that doing so involves a Molid prohibition.
Does washing ones hands with a bar of soap which contains engraved lettering contain the “erasing” prohibition?
The Ketzos Hashulchan leaves this matter in doubt although in any event the custom is not to wash at all with a bar of soap as explained above.
May one place soap into a cup of liquid and have it dissolve and then use that to wash ones hands?
Yes, as doing so is similar to placing ice in ones drink which is allowed. Furthermore one may even mix the soap into the water through shaking the vessel.
However some are stringent to only enter the bar of soap into the water from before Shabbos.
May one wash his hands with liquid soap?
Liquid soap may be used on Shabbos. This includes even if the soap is slightly thick to the point that it cannot be poured like actual liquid but is rather more like a pasty substance. [However there is an opinion which is stringent against using liquid soap even when the soap is thin like water due to the smoothening prohibition. However if one added water to the soap and it has thus already been melted down with water then it is permitted to be used according to all.] Practically the custom is to avoid using thick liquid soap.
May one use a toilet that contains toilet soap?
One is to avoid using all forms of toilet soaps on Shabbos. Thus one is to remove the soap from the toilet before Shabbos. If one did not do so it is permitted to remove the soap on Shabbos although some are stringent to remove it with an irregularity. Some Poskim however rule it is permitted to use such soaps in cases of discomfort. Furthermore some Poskim rule it is only forbidden to use toilet soaps if one intends that the soap color the water or that it release a good smell. If however one does not have intent for this to occur then one may use toilet soaps even if they color the water and release good smell.
Urinating away from the soap: In all cases it is permitted to urinate in a toilet that contains toilet soap so long as one does not urinate directly onto the soap.
Is the soap Muktzah?  Toilet soap is considered Muktzah Machmas Issur. Some Poskim however consider it Muktzah Machmas Chisaron Kis. According to this latter opinion one may not enter or remove the toilet soap from the toilet on Shabbos due to the Muktzah prohibition. It is however permitted to move it with an irregularity.
May one make seltzer water on Shabbos?
Q&A on Freezing foods/liquid on Shabbos:
May one make ice cubes, or freeze drinks on Shabbos?
May one place a bottle in the freezer so it become cold as opposed to freeze?
Yes, this is permitted even according to the stringent opinions mentioned above.
May one place liquids in the freezer before Shabbos having them freeze over Shabbos?
This is permitted according to all opinions.
May one place solid foods in the freezer on Shabbos? 
It is permitted to freeze solid foods which are normally not eaten in their frozen state. One may thus freeze cooked meat, milk and other items which are edible when not frozen.
Note: One must beware not to move any Muktzah foods while placing foods into the freezer on Shabbos.
May one freeze a liquidly food in order so it not spoil?
Yes, as this is considered a time of need in which one may be lenient.
May one enter foods with gravy into the fridge/freezer despite that they will congeal?
Yes, as since they are also eaten in their congealed state there is no Nolad prohibition involved.
May one freeze ice cream on Shabbos?
Yes as ice cream is considered like a food and not like a liquid and thus does not contain a Nolad prohibition.
May one melt ice cream on Shabbos? 
Yes as ice cream is considered like a food and not like a liquid and thus does not contain a Nolad prohibition. Nevertheless this may only be done with intent to eat on Shabbos.
Is melting fat or ice on Yom Tov forbidden due to the Nolad prohibition which applies on Yom Tov?
Some Poskim rule that all forms of Nolad are forbidden on Yom Tov and therefore it is forbidden to melt fat or ice on Yom Tov as their own individual substance. However to melt them into another substance is permitted being that it is not recognizable as Nolad.
Other Poskim rule that such a form of Nolad is permitted, and thus one may melt ice and fat on Yom Tov.
May one make ice cubes, freeze ice cream and the like on Yom Tov?
May one make ice cream on Yom Tov?
 Seemingly according to this opinion it is permitted to melt soap and fat even not into water. However salt would remain forbidden to rub and dissolve without water according to all. See 320/19
 320/19 and chapter 326 Halacha 10
 Based on mainly Ketzos Hashulchan 146 footnote 32
 M”B in name of Tiferes Yisrael, brought in Ketzos Hashulchan 127 footnote 13; 146 footnote 32. Vetzaruch Iyun from his later ruling brought in footnote below. One must say that he retracted his ruling.
 146 footnote 32
 SSH”K 14 footnote 49, in name of RSZ”A and others.
 A) It’s a Melacha which is not needed for itself [Eino Tzarich Legufa] being that the source of the Memacheik prohibition is by smoothening the skin of an animal which benefits the skin. This is opposed to here where the smoothening of the soap does not benefit the soap but rather is done for the person to use the dissolved layer. B) Since the inevitable smoothening of the soap serves no benefit, as it makes no difference to oneself whether it is smooth or not, it is therefore allowed to be done even Rabbinically, as by Mimacheik if one has no intent to benefit the item from the smoothening than it is not considered a Melacha at all, similar to the ruling regarding pouring cold water into a plastic cup [brought in “The Laws of Cooking Halacha 1 Q&A there!] C) It is done in a way of its normal use, and just like we say regarding food prohibitions that when done in its way of eating it is allowed, the same applies by soap when used in the midst of bathing.
 Ketzos Hashulchan 146 footnote 32
 As the Magen Avraham concludes with a Tzarich Iyun regarding the stringency of Avraham Halevy by engraved letters. [ibid] Now although Admur rules in 458/8 that engraved letters are forbidden to be broken, nevertheless see Ketzos Hashulchan 144 footnote 3 that this is only forbidden when one breaks it and then eats it, if however one breaks it within the process of eating it is allowed. Thus perhaps here too there is room to question whether erasing the letters in the process of using the soap is truly forbidden.
 Ketzos Hashulchan 127 footnote 13
 As explained above in Halacha 2 Q&A there, based on Ketzos Hashulchan 127 Footnote 2. So also rules SSH”K 14/16
 Ketzos Hashulchan 146 footnote 32
 SSH”K 14/16 footnote 49, based on Ketzos Hashulchan 138 footnote 31 with regards to using toothpaste. So rules also Ketzos Hashulchan explicitly in 146 footnote 32; See also Shabbos Kehalacha Volume 3 17/73
 As it is already a liquid and the bubbles that it creates have no significance.
 Igros Moshe 1/113
 So rules Az Nidbaru 1/16 brought in Piskeiy Teshuvos 326/8
 Shabbos Kehalacha Vol. 3 17/73
 Orach Yisrael 35
Background of the prohibition:
The use of toilet soaps may involve any of the following three prohibitions: Molid Reiach; Nolad and Tzoveia [dyeing]
- Prohibition of Nolad: Seemingly it is forbidden to use toilet soaps due to the Nolad prohibition being that one is melting the solid soap thru flushing the toilet [which is similar to urinating on snow which was viewed as if one is melting the snow with ones hands]. Thus even using unscented and non-colored toilet soaps would be problematic. [Orach Yisrael 35 rules based on this reason that initially it is forbidden o use toilet soaps unless it is a case of Shaas Hadchak] However there are Poskim which rule that there is no issue of Nolad with toilet soaps as it is only a minute amount which melts, and that itself is through an indirect action.[Shabbos Kehalacha Vol. 3 17/80]
- Prohibition of Tzoveia: If the toilet soap releases a color into the water, then it may not be used due to the dyeing prohibition. [SSH”K 23/14] However some Poskim allow its use if one has no interest at all in the coloring of the water. [Shabbos Kehalacha Vol. 3 17/80]
- Prohibition of creating a new smell: The prohibition of Molid Reiach does not apply even when using a scented toilet soap. [Practically although Poskim [Sharreiy Teshuvah and Mishneh Berurah in 128/6; Minchas Yitzchak 6/26] rule it is forbidden to create a good smell in water, nevertheless it is allowed to absorb a good smell into the toilet water as the good smell is simply there to remove bad odor. [Beir Moshe 1/34 rules that good smells may always be applied in order to remove bad odors, and so rules Piskeiy Teshuvos [327/1, 328/26] Other Poskim however rule it is only allowed if one has no intent to create a good smell within the water. [Shabbos Kehalacha Vol. 3 17/80]
 See below and Shabbos Kehalacha Vol. 3 17 footnote 196 for a discussion on the Muktzah status of the soap.
 Orach Yisrael 35; Shabbos Kehalacha ibid, there he extends the leniency to even toilet soaps that dye the water.
In Sefer Orach Yisrael 35 he rules that one may be lenient to use such soaps if lack of doing so will cause bad odors and distress, as he rules that in a Shaas Hadchak one may be lenient like the opinion which holds that melting soaps and fats do not contain a Nolad prohibition. Furthermore he rules that if one forgot to remove it before Shabbos then it may be used on Shabbos being that it is Muktzah and is forbidden to remove and thus this case too is a Shaas Hadchak. Vetzaruch Iyun according to Admur why he rules by melting fats near fire that one is to be stringent unless it is a Shaas Hadchak while here by soaps he plainly rules that one is to be stringent [implying even in Shaas Hadchak].
 Shabbos Kehalacha ibid
 Shabbos Kehalacha Vol. 3 17/81
 Shabbos Kehalacha Vol. 3 17 footnote 196
 Igros Moshe 5
 Minchas Yitzchak 4/122; although it is best to do so from before Shabbos [9/33]; SSH”K 11/35 in name of Rav SZ”A; Mahrsham 3/140; Ketzos Hashulchan 138 footnote 31
 Bris Olam Ofeh 91; Chelkas Yaakov 3/168; Tzitz Eliezer 7/24
 SSH”K 10/4; Piskeiy Teshuvos 320/4
 Poskim which permit: Rav SZ”A, Betzeil Hachachmah 2/25 rules that if one’s entire intent is to re-melt the ice and then drink it then it is permitted, thus by ice cubes it would be permitted, although by ices forbidden.
Poskim which prohibit: Doveiv Meisharim 1/55, Mishneh Halachas 4/48
 So is the final ruling in SSH”K, as well as in Mishneh Halachas. It is permitted to do so in a case of need as this is similar to placing ice in an area where it will melt which Admur rules may be done in a case of need. This is in contrast to the Doveiv Meisharim which rules that even in time of need it is forbidden as all opinions agree by freezing that it has a Nolad prohibition, and it was only regarding melting that the dispute was brought. However many Poskim argue on this and say it retains the same dispute. [See Piskeiy Teshuvos ibid footnote 14]
 Az Nidbaru 10/8
 As although it may begin to freeze a little before one remembers to remove it, nevertheless since the entire prohibition of freezing items is itself only stringency, therefore here it is allowed.
 Chelkas Yaakov 2/98
 SSH”K 10/5
 Minchas Yitzchak 8/24
 Piskeiy Teshuvos 320/4
 SSH”K 10/7
 SSH”K 10/8
 Shut Mahrsham 6/33; Doveiv Meisharim 1/55; Shevet Hakihasi 3/170
 SSH”K 12 footnote 29 in name of Rav SZ”A.
 511/7-KU”A 1
 So is implied from Admur ibid, and so understands Piskeiy Teshuvos 495 footnote 48
 So rules Chelkas Yaakov 2/98; Piskeiy Teshuvos 495/10.
As a) Nolad does not apply by food on Yom Tov. [Admur in previous question]; b) According to many Poskim making ice on Shabbos is not clearly a problem of Nolad and thus they allow it to be done in times of need, thus here by Yom Tov where it is even questionable whether Nolad applies to foods at all one may be lenient.
 As Admur rules [511/7] that Nolad does not apply to foods on Yom Tov.
 Doveiv Meisharim 1/55
 SSH”K 10/6
 As kneading is permitted to be done on Yom Tov.
 As anything which could have been done before Yom Tov without having its taste or quality diminished may only be done on Yom Tov with an irregularity. [Rama 495/1 Admur 495/5, and so rules M”A and M”B] Vetzaruch Iyun Gadol on SSH”K ibid which did not mention that an irregularity is needed. As well Tzaruch Iyun on Piskeiy Teshuvos which adds that an irregularity is needed if one had time to do it before Yom Tov, as it is ruled [Admur 495/6; M”B 495/10] that only in a case of “Ones” may one do it on Yom Tov without an irregularity. However if no “Ones” occurred, even if one forgot to do it before Yom Tov, it may only be done on Yom Tov with an irregularity.
 Piskeiy Teshuvos 495 footnote 52 based on the many Poskim which rule that making ice cream contains a Boneh prohibition which is equally forbidden on Yom Tov.