Backtagging: Yes please
Threadhopping: Sure
Fourthwalling: Yes. You may get an upset Thing out of it if you're not careful, though, because he'd rather not get caught
Other: Palmer is a stoner, if that bothers anyone.

Hugs: He may be a little startled, but he'll accept it from a friend
Kissing: Saliva is a bodily fluid. All of his fluids are extremely infectious alien pathogens. Do not kiss.
Fighting: Palmer is a Thing, which means that you really don't want to see how he reacts to being cornered. A more minor fight won't break his cover, but he avoids them unless he's trying to transfer suspicion to someone else.
Injuring: This would probably require high explosives, or at least a flamethrower. He can heal well enough that I’m not against it, though.
Killing: Unless you freeze every bit of him and keep it in cold storage that's going to be pretty much impossible. Even then he's just on hold. Unless you have a way to destroy every cell in a person's body at once, anyway. So that probably won’t come up.