Replacing the whole housing is the easiest option, but if you want to replace the glass, heating the back is possible, and some people say cooling the phone with liquid nitrogen is easier, although both are intentionally extremely hard.
The screen is definitely replaceable. The only thing though is that the screens are very expensive, costing upwards of $300 sometimes, depending on the quality. The “iPhone is Disabled” message usually happens when the phone’s internal clock resets due to an extremely discharged battery, though it could be a different cause, and can be fixed by connecting to iTunes and restoring it by going into restore or DFU mode. As for the phone not ringing out or charging, that seems like a problem with the speakers and lightning port. Overall, this phone seems to be very abused, and likely will be very costly to repair. You could take it to Apple and see if you can get it repaired or replaced, or you can go Third-Party, and although it will likely be cheaper, the parts might not be the best quality. Since the phone is new, I would recommend going to Apple instead. Next time, though, get a case and screen protector. Rhinoshield makes great quality screen protectors and cases.
This is a problem with the LCD or the connectors. I would reccomend if you are able to clean the contacts on the motherboard for the LCD, do so. If that doesn’t work, you’ll need a new LCD. This happened to my friend’s S5. If you have a Micro-USB to HDMI adapter, try using that to see if the phone works fully, since now you can get them for pretty cheap.