According to Chabad custom, must one be careful not to take three steps back if the person in the back of him is still in middle of Shemonah Esrei?
Yes, as is the ruling in Shulchan Aruch, which is binding on all Jewry without exception, and thus the question itself is most puzzling. In fact, the Alter Rebbe was so particular in this matter that he writes that one who doesn’t follow it will be banished from having audiences with him.
Sources: See Admur 102:5; Shut Admur 12 Takanos Tefila and Takanos Liazna
How important is it to give an exact report to the insurance company, and may one exaggerate expenses, or not report negligence, in order so the insurance covers more costs?
It is biblically forbidden to do so due to the stealing prohibition, whether the owner of the company is a Jew or Gentile. One must give an exact report to the company, and may only receive reimbursement for money that he is entitled to under the contract, based on the true events that occurred.
Source: See Admur C.M. Hilchos Gezeila Ugineiva Halacha 1-4
Should a divorcee who was only married for a few months continue to light two candles by Hadlkas Neiros Shabbos, or should she only light one candle?
She should continue to light two candles.
Source: See Piskeiy Teshuvos 263:2
With which hand is the Baal Korei to use to hold onto the Eitz Chaim of the Sefer Torah while he is reading?
Although during the actual blessings of the Aliyah, the Olah is to hold onto the right handle using his right hand and left handle using his left hand, and the Baal Korei is likewise hold onto the left handle during the reading, no preference is recorded in the Poskim regarding which hand the Baal Korei is to use to hold onto the left handle, and therefore he may choose whichever hand he wishes, although usually it is easier to use the left hand. However, in the event that the Baal Korei receives an Aliyah, then he is to only hold onto the right handle using his right hand.
Source: See Michaber 147:1; M”A 139:13; Kaf Hachaim 139:24; https://shulchanaruchharav.com/halacha/holding-onto-the-handles-of-the-sefer-torah-during-the-aliyah-why-and-how/ and https://shulchanaruchharav.com/halacha/chapter-4-the-baal-korei/ ; https://shulchanaruchharav.com/halacha/chapter-4-the-baal-korei/
This matter is under debate, and practically one is not to do so, and so rule many leading Chabad Rabbanim.
By a whole cake that has yet to be cut, should one say the blessing prior to cutting the cake, or should he first cut off a slice and then say the blessing on the slice?
The blessings to be said prior to cutting the cake at all.
Source: See Admur 167:3
May one spill the liquid out of cans on Shabbos or is doing so prohibited due to the Borer prohibition?
One is not to do so if contains small sized content, such as olives, although one may do so if the content of the can is large, such as pickles which are not cut.
Yes, although it is best to remove it before Shabbos.
Yes, from the letter of the law, however, there is a Hiddur to not support such businesses. However, in this case one must also balance the fact that if is boycotted by religious people then it will be open for mixed genders all the time breaking the laws of Tzenius.
Source: See Piskeiy Teshuvos 245:9
Only through a gentile, and even then he should replant it elsewhere, except in Eretz Yisrael during Shemita in which case it should be removed with much earth and simply placed in a pot.
See here regarding uprooting a fruit tree: https://shulchanaruchharav.com/halacha/destroying-a-fruit-tree/
See here regaridng shemita: https://shulchanaruchharav.com/halacha/from-the-ravs-desk-in-eretz-yisrael-may-one-uproot-a-tree-during-shemita/
If there is no Minyan in Shul, may and must the congregation remove the Sefer Torah and read from it without the blessings
They may if they wish, however, they are not required to do so. Whatever the case, each individual should read the Parsha to himself.
No it does not, and thus it may be used for mundane objects.
One is to wipe with it and without tearing it, place it into the toilet and then flush.
See here for all opinions and details: