Not sure why you sent a rooted phone back to a Sony service center. It would have taken all of twenty minutes to wipe it and put a stock rom back on, then there would have been no issues with warranty.
Not unless you had lost your TA keys.
I had my screen replaced by Sony for free. I had to un-root my phone before I sent it back, but you should factory reset your phone before sending it to any repair shop, you wouldn't want any strangers looking at your pictures/contacts.
A new Z1c screen should cost $50, there are lots of screen change videos on youtube, why not fix it yourself?
LCD+DIGITIZER the exact replacement part. Yes, i'll try to locate myself too.