How do I remove these bathroom faucet fittings with limited space?
First - Remove the chrome apron and see if there is a top nut holding the fixture from the top.

If the faucet cannot be removed from the top, then use this method.  Since you are replacing the faucet, I would just cut the copper pipe at the Tee inlet as shown in my picture or close at the end of the thread.  Do the cut which would allow you to unscrew the fitting.  Once the fitting is removed, then a plumber socket can be used to loosen the retaining nut.  I have done this on several faucets for friends who were replacing their fixtures.