"It appears that the BBC owns the name "Top Gear," so if Clarkson & Co. jump to another network (or go independent), they'll need a new name. If the BBC owns the name, then one has to wonder how much they also "own" the format. Can Clarkson & Co. produce the same show under a different name, or will they need both a new name and a new format?"
Of course BBC owns the name. You don't run a show that successful and not own the name. That would destroy your ability to monetize it. Top Gear America, Top Gear German, Top Gear Australia, etc., all pay substantial fees to the BBC (or, more realistically, the networks that host those shows in their respective countries).
BBC likely also owns the representation of the mystery racing driver, so that would be dicy if they could do something like that. They could also claim ownership (at least of the names) over Star in a Reasonably Priced Car, the Cool Wall, and a few other things that originated on Top Gear.
As for the format, that's a lot dicier to try to claim ownership over. It's a car show, and there have been LOTS of car shows over the years, even before BBC came along with theirs. Could BBC try to claim the "testing the cars on a closed circuit"? They could, but it would be a big fat fail. Track tests have been a common element.
The biggest concern would be if their contracts had "no compete for X years" clauses. That could prove to be a significant issue.
The last 3 programs in the current series could be intersting. After Clarkson was suspended, BBC went to Hammond and May and asked them to continue with filming the finishing touches, which normally involved all three of them. Both of them refused to do so until the issue with Clarkson was resolved. If they continue to do so, it could constitute breach of contract, which could lead to litigation.
As for the physical attack, an article on BBC News says that Clarkson apparently popped the guy in the mouth hard enough that he felt it necessary to visit an emergency room.
There was also mention of protracted, extreme verbal abuse towards the producer at the same time.
Given earlier reports, it's likely that Clarkson was drunk and was acting out. I've seen other mentions over the years that he gets... boisterous, and not always in a good way... when he's been drinking.