I don't think it was as simple as Nick locking his door; as
shazba said, his room did take some damage.
But I agree about the rest. Nick as a mole makes little sense. If he were mad at the DIKs for whatever happened with Vinny, he would have left when Vinny did. Rusty isn't some mastermind whose plans can only be disrupted from within! Combine that with the fact that he didn't have access to the Jade video and I see most of the evidence against him as classic DPC red herrings.
It's possible Nick is inadvertently revealing DIK secrets to Vinny, not realizing how much of a grudge Vinny has against his former brothers, but that's as far as I think it would go. Hopefully we'll find out the truth soon, but the way the game has been going it feels like we're in for a long wait before DPC starts tying up the loose plot threads.