Can someone wind an already ticking watch on shabbos? What about a self winding watch that winds with hand movement?
This is a delicate question. The main reason why poskim forbid winding a watch on Shabbos is that it is considered “fixing a vessel,” or, according to the Chazon Ish, an act of “building.” In the case of a ticking watch, neither of these reasons apply, and the Da’as Torah 338:3 writes that the custom is to be lenient. However, the Mishnah Berurah (338:15) is stringent even regarding winding a ticking watch, and this is the accepted custom (see Shemiras Shabbos Kehilchasah 28:19), unless there is an urgent need.
There is no problem in wearing a self-winding watch while it is ticking. See Shemiras Shabbos Kehilchasah 28:28, and sources cited in the footnote.