A1: You can sell your players and your players also show up on the transfer market. There are certain conditions that do not allow you to sell your players:-
1)You have reached minimum number of players for your team.
2)Player you wish to sell may retire next season.
As for their names on transfer market, they always appear. Condition is you must press R2 and fill up correct details.

A2: You can only sell people when it is the trade season that only goes for a limited time on the game not to be sold!