Do you think my boyfriend cheated with the girl at his house?

First off I think if you felt the need to spy on your bf then there are clearly huge trust issues in your relationship. Second, I feel like the best way to figure out is ask the girl's bf if he knows your bf and if he seems to trust him with letting his gf sleep at his place then I'd say you can trust him too. Concerning his lies, I wouldn't be worried about him saying he was back earlier than he really was, thats a lie everyone says when they go out. If he lied about him hanging out with a dude, I think its kind of a toss up, because even if nothing happened he'd probably still say it was a guy just to avoid suspicion