Yeah, but in the case of the car, it's not offering free promotion for mom's TV show.
(God, I made that into a horrible analogy).
Assuming he's not profiting from the web series, I can't see NBC/Universal or Sony doing anything to stop him.
It depends. If they think he is HURTING their brand, yeah, that would give them reason. (Of course, how do you hurt a brand of a very low rated show... but, there you go.) And who knows, maybe Dan Harmon has ideas on what HE wants to do with Inspector Spacetime.
In the end, I agree, I don't think they will do anything to stop him, I won't be surprised if they do. The actor doesn't own the character. Or the trademark. Any of it.
And this is a little different than fan films of Star Trek. Shatner wasn't out there making fan films while Star Trek was still on. And by the time Stark Trek alumni started appearing in fan films, there were already a LOT of fan films setting a precedent of Paramount's tacit agreement on them.
I wish the actor luck. He should tread carefully.