May one ask a gentile to untie a temporary knot in a time of need?
May one make a knot which is usually not undone that day if he intends to undo it that day?
May a knot with a bow on top be made on a disposable bag or the like which one plans to throw out and never actually undo?
If ones Tzitzis became tied onto another person’s Tzitzis, may it be undone?
According to above answer it may only be undone if the knot is not tight.
If ones shoes became tied in a double knot and he cannot remove them may he undo the knot?
Even if the knot is tight one may undo it, as in a case of pain we allow to untie double knots.
May one make a single bow to last forever?
May one make a tie on Shabbos?
If not made in way of a double knot [or any type of tight knot] then it is allowed when done to untie within 24 hours.
If the tie was made before Shabbos in a double knot, then it may nevertheless be loosened and tightened.
May one tighten his Tzitzis on Shabbos?
No and does so it is possibly a Biblical prohibition.
May one wind or unwind twist-ties on Shabbos?
Some Poskim rule it is forbidden to do so. However there are authorities which defend the widespread custom to allow doing so on the basis that here one has no true intent to make the twist tie into a rope.
May one tie a bandage onto a wound?
One is to do so through making a bow over a single knot, and not through a double knot, as doing so may involve the tying prohibition. If however it is not possible to make a single knot with a bow then if one is in pain one may make a double knot with intent to remove that day, or at the very least in a time of need within seven days.
 Levushei Serud on Taz 317/5, as is ruled in 307
 See footnote above which dealt with this issue.
 So is implied from Admur 317/1: However knots that are always for certain left [tied] for a certain amount of time and it is never usual to untie it that same day, then it is forbidden to tie them on Shabbos even casually or to untie them.
 Rav SZ”A brought in Piskeiy Teshuvos 317 footnote 24. However in Minchas Yitzchak 8/27 he brings that Rav SZ”A ruled to him that when the item is thrown out it is considered destroyed, and thus should be allowed. However it can be implied from Admur 651/6 which considers the knot of a Lulav made to never be undone, even though after Sukkos it has no use, that throwing out is not considered like destroying. However see Tzitz Eliezer 15/17 which explains that possibly one keeps a Lulav to inherit to his children. Vetzaruch Iyun.
 Minchas Yitzchak 8/27;
 Mishneh Halachos 3/38
 Michaber 5. Ruled in Ketzos Hashulchan 4. In footnote 11 he leaves it with a Tzaruch Iyun why the Alter Rebbe did not mention this here.
 SS”K chapter 15 Halacha 58
 Piskeiy Teshuvos
 Ketzos Hashulchan 123 footnote 4. However if done to untie that day then even to make the entire Tzitzis initially is only Rabinically forbidden. Now although one is doing so for the sake of a Mitzvah, nevertheless this was only allowed by an item that is normally eventually untied while by Tzitzis we suspect that he may leave it there forever. [Peri Megadim brought in Ketzos Hashulchan 123 note 9]
 Piskeiy Teshuvos 317
 SS”K [chapter 9 Halacha 13] writes that tying or untying twist-ties is forbidden on Shabbos if done strongly due to that this is similar to raveling threads together into a rope, which is forbidden due to the tying prohibition. It is therefore likewise forbidden to undo.
 Sheivet Halevy
 Piskeiy Teshuvah 328/21, see also Tzitz Eliezer ibid which writes that a bow knot is to be made.
 However there in Piskeiy Teshuvos he writes “if the bandage is a type which is meant to be removed that day”. However based on chapter 317/1 -2 it makes no difference if the bandage usually is made to last more than one day so long as ones intent is for it to last less than one day.
 So is implied from Admur 317/1-2. Vetzaruch Iyun as there Admur only permits for a gentile.