I don't know. I think that Jamie was offering John the only thing of value that he had, himself, knowing that John wouldn't accept. In a later book, he tells Claire that it was a test to see if he could trust John with Willie. If John had accepted, he, Jamie, would have killed him. He does fleetingly kiss him, though, and then says something like, "I'm maybe not poisoned, then."
I think that they respect each other a lot. You can watch their relationship develop in the side books, which give you a nice bit of background. Poor John never truly moves on, though he does have other relationships, a couple of them deep and meaningful ones.
I| thought that Jamie looked quite good in that wig, it was certainly better than the awful ones that he was wearing at the start of the season. It did a mighty fine job of showing of his bone structure and the whole point of it was to hide his red hair. I think Geillis's one was supposed to be an obvious wig, part of her formal ball attire. Huge wigs were a thing in those days, I think.
The whole get separated, get rescued thing goes on all through all the books. SOmetimes, I think, for ony peace, can DG not think of something else to do? Can they not just live quietly for a while. BUT, the snatches of happiness keep you hooked.