Yes, a TA can charge you for these changes. You had separate tickets. It is very possible each fare basis was booked for your new flights so the TA had to 'buy up' to the next available fare basis - and this would be in addition to the change fee itself. If this was the case, you had 4 fees because you had separate tickets.

As far as the cc, maybe they were afraid of you disputing the charge after your flights.