In this scenario, Batsman B is out - as they have not crossed on this run, his ground is where the wicket has been broken, and so he's out.
This is covered by Law 38.3:
The batsman out in the circumstances of 38.1 is the one whose ground is at the end where the wicket is put down. See Laws 25.6 (Dismissal and conduct of a batsman and his/her runner) and ...
The answer is “no”.
18.104.22.168 a fielder catches the ball after it has been lawfully struck more than once by the striker, but only if it has not been grounded since it was first struck. See Law 34 (Hit the ball twice).
As long as they are part of the playing XI (including any made concussion substitutes), they should be able to bowl, as there does not appear to be any rules stating against this.
From the ICC T20I Playing Conditions*:
Only nominated players in the match (including activated concussion replacements) may participate in the Super Over. Should any player (...