If one is married and wears a tallis, then when it comes to mincha on a fast day and one gets an aliya, does A) one make a bracha on the tallis, and B) when does one take it off, as I heard its after kedusha. What are the sources for this? Thank you.
If one wears one’s own tallis, a beracha is made. If one wears a community tallis, one should have intention to make a “acquire” the tallis, and preferably wrap himself in the tallis — and a berachah is made (Mishnah Berurah 14).
The Ashkenaz custom was to take off the tallis, after wearing it for an aliyah on minchah of Shabbos, only after kedusha.
It is possible that the source for this is that one should wear the tallis for a considerable period of time, so that the wearing should not be merely for the honor of the community, but also for the sake of actually wearing it. As the Biur Halachah writes (14, s.v. she’elah, citing from Shaar Efraim and others), for the sake of making a berachah the tallis must be worn for the sake of wearing.