Believe Apple charges $129 if I'm not mistaken. I wouldn't personally trust anyone else myself. And you would retain any existing warranty.
Yeah I was thinking that although the phone is already out of warranty. I fixed a 4S a few years ago at a local shop for $40 but I assume it costs more to replace the 6's screen.
The screen is shattered and the right side of the screen can be unresponsive most of the time. The back of the phone is perfectly fine.