Q: Two PSN accounts and games on HDD

I bought a used PS3 with active PSN account and some bought digital games on HDD.

If I'll register a new PSN account, would I be able to play these installed games (or they are locked to one PSN account)?

I'm pretty sure they are under that other account? Why are you using someone else's logged in account? lol. They could remotely cut the cord on that at any time. Your best bet is to use your own. That's not to say that you probably could switch back and forth between two accounts to play games, I suppose. That sounds a bit inconvenient, but probably the best route at this point.