The law of one which is bedridden or feels weak in his entire body but is not in danger:
Having a gentile do forbidden work: A sick person that is bedridden due to his illness and is not in danger or [a person] that has an ache that pains him to the point that his entire body is weakened due to it, in which case even though he is able to walk he is considered like one who is bedridden, then all of his needs may be done through a gentile, even complete Biblical prohibitions such as to bake for him or to cook for him if he needs this done.
[Regarding giving assistance to a gentile which is giving the medical treatment-See Halacha 8]
The reason that Bishul Akum has been allowed: Now, although all forbidden foods, even those [forbidden only] Rabbinically, were not permitted for a sick person that is not in danger [to eat from them], nevertheless [the Sages] permitted [this sick person] on Shabbos in which there is no other available option [to eat food cooked by a gentile which contains the prohibition of ] Bishul Akum due to that the food is permitted in it of itself and it is only that an action of the gentile is causing its prohibition.
The prohibition for a Jew to Biblically transgress: However a Jew may not transgress Shabbos in doing a Biblical prohibition even if there is danger of [losing] a limb [and certainly if he is merely bedridden or weak], so long as there is no danger of life.
The allowance for a Jew to Rabinically transgress with an irregularity when one is bedridden: [Although when there is danger of a limb a Jew is allowed to transgress Rabbinical prohibitions in their regular fashions, nevertheless] if there is no danger of a limb, then although he is bedridden or is in so much pain that his entire body feels weak, we do not allow a Jew to do something for him which is Rabinically forbidden unless done in an irregular fashion then the normal way that it is done during the week.
Doing even Biblical prohibitions with an irregularity: [Furthermore] when doing an irregularity it is allowed to even do a Biblical prohibition [see footnote for other opinions] [if it cannot be done through a gentile], such as for example one who is moaning [in pain from the heart] (of which it is permitted for him to suckle the milk of an animal) with his mouth as will be explained, as since he is changing from the regular way in which it is done it is only Rabbinically prohibited.
Medicine for one who is bedridden: However if one needs to eat foods which are recognizable that they are administered for healing, then although doing so is a Rabbinical prohibition due to [a decree] that one may come to grind up herbs as will be explained [in Halacha 43], nevertheless since (this is something which is impossible to do through a gentile and he is) sick throughout his entire body, [therefore] [the Sages] permitted for him to do so.
Other Opinions: [However] there are opinions which prohibit [the ill person from taking medicine].
The Final Ruling: Regarding the final ruling, in a [dispute over a] Rabbinical prohibition one may follow the lenient opinion.
Making medicines: If one needs to prepare the medicine, such as to mix a medicinal ointment together, then it may only be done using an irregularity. Thus if one needs to make an oil/wine mixture it may not be mixed on Shabbos and rather one is to place each liquid separately on the required area. The reason for this is because it is forbidden to do any prohibition, even Rabbinical, without an irregularity if the patient is not deathly ill.
Summary-A person which is bedridden or feels weak in his entire body:
Having a gentile do the treatment: All prohibitions needed to be done in order to treat him may be done through a gentile, including even cooking and baking, which presents aside for a Shabbos prohibition, also a Kashrus prohibition.
Having a Jew do the treatment: It is permitted for a Jew to do any prohibition, even Biblical, when it is done with an irregularity [although a Biblical prohibition may only be done with an irregularity if it cannot be done through a gentile]. A Rabbinical prohibition too may only be done with an irregularity.
Taking medicine: One may be lenient to allow medicine to be taken, even though doing so is a Rabbinical prohibition done without an irregularity.
Making medicines: If one needs to prepare the medicine, such as to mix a medicinal ointment together, then it may only be done using an irregularity.
In cases that an action may only be done with an irregularity, what is defined to be an irregularity? 
One is to ask a Rav what is considered an irregularity for each particular forbidden action that he must do.
Is a Biblical action not done for its own use considered a Rabbinical action and allowed to be done by a Jew in cases that only a Rabbinical action is allowed to be done?
No. It is considered like a Biblical action being that it appears like one is doing an actual Biblical prohibition. [However to ask a gentile to do so in cases that only Rabbinical action may be done by a gentile is allowed according to those which hold that it is only considered a Rabbinical action.]
May one who is bedridden or weak in his entire body take medicine for a mere ache?
No. Medicine may only be taken for those symptoms that cause him to be bed ridden or weak in his entire body.
Do the leniencies of a bedridden person apply even if he caused himself to reach this state, such as a failed suicide attempt?
Some write that in such a case he may not be lenient in any of the Shabbos prohibitions.
May one take medication if he suspects that lack of doing so can lead to being bedridden or weak in his entire body?
May one ask a child to do Melacha for a non-dangerously ill person who is bedridden?
A Biblical prohibition: No. A child has the same status as an adult in these regards. Hence just as an adult may only do a Biblical prohibition with an irregularity, and only if a gentile is unavailable, so too a child may only asked to do so in these circumstances. This applies even if it is the child himself which is ill and is being asked to do Melacha for his own treatment.
A Rabbinical prohibition: If no gentile is available [and one cannot do so with an irregularity] seemingly one may be lenient to have a child do so, on his own behalf, such as if the child is sick. However on behalf of another that is sick it requires further analysis if the child may do so. In all cases if one can do so on his own with an irregularity then one should not ask a child to do so without an irregularity.
May a child be asked to plug in or turn on a nebulizer for one who needs it?
No, unless it is a matter of danger or can lead to it, in which case even an adult may do so, and it is even better that an adult do so. This includes even if the child needs it for himself.
Doing so with an irregularity: It is however permitted to be done with an irregularity, even by an adult, for one who is bedridden, if no gentile is available. It requires clarification as to what would be considered an irregularity in this case.
 Now, although earlier we stated that one may ask a gentile to do even a Biblical prohibition, which itself is a Rabbinical prohibition, nevertheless there this is because the Jew is merely commanding the gentile to do so and is not doing any action and thus the Sages were not as strict to require the gentile too to do a Biblical action with an irregularity. [Ketzos Hashulchan 134 footnote 5]
 As rules Admur so rules Igleiy Tal Tochen 18; Tehila Ledavid 22.
However the M”B  rules that only Rabbinical transgressions may be done with an irregularity and not Biblical transgressions.
Regarding the reason for why according to Admur a Rabbinical transgression may only be done with an irregularity while a Biblical transgression done with an irregularity [which is considered a typical Rabbinical transgression] is allowed-see Ketzos Hashulchan 134 footnote 6.
 Ketzos Hashulchan 134 Halacha 4
 Meaning that here the prohibition is in the actual eating the medication which is something that only the patient can do, and thus should ideally be prohibited due to that it cannot be done with an irregularity, nevertheless this itself is the reason to permit it as there is no other way to administer the medication.
 Ketzos Hashulchan 134 Halacha 4
 Ketzos Hashulchan chapter 134 Halacha 4
 Ketzos Hashulchan chapter 138 footnote 5
 As rules Admur in Halacha 3
 Igros Moshe 5/51
 Piskeiy Teshuvos 329/1
 Tzitz Eliezer 10/25
 SSH”K 34/16; Piskeiy Teshuvos 328/2
 As it is a Biblical prohibition to ask a child to transgress Shabbos or do any sin. [265/10; 343/5] Hence asking a child to do a Biblical prohibition which is forbidden for an adult does not make it any more lenient, and hence is not allowed.
Background of above ruling:
In 343/5 Admur rules it is Biblically forbidden to feed a child any Issur, although it is unclear from there if other Issurim are as well Biblical. However in 265/10 Admur states explicitly that asking a child is Biblically forbidden.
VeTzaruch Iyun based on this from 328/134 that implies that asking a child to transgress Shabbos in a case of danger is better than having an adult do it, hence implying there is no Biblical prohibition involved in asking him!!
A. Perhaps one can say that the Issur in asking a child is not in having him do the transgression but in asking him to do something which he is not allowed to do. However in a case of danger since even a Jew may do so, asking the child is not forbidden at all, and hence there is no prohibition at all taking place, as the child is not commanded in Mitzvos and the adult was allowed to ask him. If however an adult transgresses, then although it is allowed and a Mitzvah, it is merely Dechuyah and is similar to an amputation which is done to save one’s life.
Hence the advantage of asking a child is that it goes from dechuyah or Hutrah
 As otherwise it is better for one to do so with an irregularity which is permitted according to all by a Rabbinical prohibition in case of a bedridden person, and not enter oneself in a dispute regarding having a child do a Rabbinical prohibition for his own sake.
 As the allowance in 343/6 is only for the sake of a Mitzvah. Vetzaruch Iyun if a bedridden person can be equated to the sake of a Mitzvah to be lenient.
 As electricity is viewed as a Biblical transgression, and asking a child is Biblically forbidden as explained above.