Yes, they do, it happen just after they stopped being vigilantes. After that, a lot of stuff happens, such as them being a backup dancer on a J-pop concert and stuff (with a disguise of course). Chifuyu always thwart their effort
Note 1 - Yes, since there's no other means unless Joshua use the day they met as his birthday.
Note 2 - Him entering I.S.A. is a mean to protect him from harm (Excuse plot at the finest point indeed), he never talk about career after it. This is the reason of which, why he must go to college in Sacred Twins, in order to become a proper teacher.