I wouldn't ride it at all until confirming the front wheel bearings are good. Again, front wheel needs to be off the ground, stand on one side, grab the tire at the top and try to push and pull, if there is side play, they need to be changed. I had one that was so bad, you could see the wheel moving side to side as the brake was applied, I suspect that is how the PO wrecked it. If the bike shakes when you're pushing it, something is very not right. Bearings and brake pads are cheap, many people switch to tapered headstock bearings for smoothness even tho the stock ones aren't damaged. If you really want to get to know your new baby, take the front end apart and replace everything that can be replaced, then you'll know for sure.