1. Belts......don't just check them...replace them. I used to keep at least 5 for each axis in stock all the time. They sometimes look good....but the teeth get damaged from one or two collisions. Buy them from SDI....they are about $3 each. The newer DHC and DHC2 machines from PlasmaCam have more robust belts...and don't have this issue.
2. I never had trouble with this...but many users have reported pulleys slipping on motor shafts. Set screws may be loose.
You can make a pen mount...and draw the header flange on a piece of paper with the machine to see if it looks better that way. Have you checked the torch carriage to see if the pivot points (where it flexes to activate the limit switches) are broken? I had to weld mine more than once....again, the newer PlasmaCams don't have this issue.