What is the bare minimum for Tzitzus to be Kosher? I know, for example that each corner needs 8 strings (but 7 is also Kosher). What about for example the five knots?
The five knots aren't a strict halachic requirement, but rather a custom. Technically, even one winding and one knot is enough. However, this should be relied on only in emergency cases, such as where it's right before Shabbos and there is no time to fashion the tzitzis properly. (Magen Avraham, Orach Chaim 8:19)
7 strings is only kosher if the string is cut off until the last knot. If it is snapped further up then one must determine that there are 4 thumb-widths left of the string before the hole on the beged. 6 strings is also kosher if both strings that are snapped are on the same side of the last knot provided that one kept the 4 strings on each side clearly separated when tying the tzitzis in the first place. If a string is snapped by the hole where they are attached to the beged, without 4 thumb-widths of it remaining then that tzitza is posul.
(Kitzur Shulhan Aruch)
When you make them: (assuming you buy kosher tzitzit- i.e. they don't come from a sheep which was worshipped as an avoda zara)
- They are required to be 4 strings folded over.
- They must be at lease a tephach long, and ideally 3 tephachim when they are folded over.
- They must have been tied onto the talit- they cannot have been prepared before and then attached.
- Ideally it should be 1/3 knots and loops, and 2/3 loose strings. Based on the measurements given above, ideally it should be at least 1 tephach knots and loops and 2 tephachim loose strings (but to be strictly kosher, they only need to have two knots and 3 loops).
If, after this point, they tear:
- Every string (of the original four) must be long enough to be able to tie in a knot. Therefore, if one string tears all the way down to the knot, it is still valid. If two of them tear all the way down to the knot, we are concerned that perhaps they stem from the same string (remember, each string is folded into two) and the tzitzit are invalid. If, when you tie the knots, you keep track of which strings stem from which base string, such as by keeping one side of the original 4 on the same side of the knot, then even if 4 strings tear down to the knot (on the same side of the knot), as long as the other four are long enough to be tied in a knot, they are still valid.