Yo! So did you hear about the fast food joint who had traces of pork in their vegan patties? Press refers to the incident as the ham veggy burger gate.
I don't see how Marten has fallen for Claire. I don't see how they have any sort of special connection. I mean, he tried to go with Faye, Dora, and Hanners first, and the only reason he invited her to the wedding was because she had a car.
She may have offered the ride as a thanks for the treatment at the party, or because she liked the idea of spending time with him, or maybe she was just bored. Either way, I doubt he accepted just because of the car - Claire just offered a ride, and he invited her to the wedding, and it's not hard to imagine that he really preferred her company over going alone.
The wedding strengthened their friendship. Time spent together, new experiences gained together. Besides the on-panel events, #2405 references quite a few off-panel events as well.
The cuddle (and its aftermath) may look like "everything went back to normal", but it did two things. First, it taught them that they can be honest with each other and work through issues. That alone is something he and Faye didn't have for a very long time, and even with Dora "working through issues" involved a lot of shouting and drama. Second, I think it forced both of them to consider whether there was more than friendship. Of course, neither dared act on it, but that wasn't "back to normal".
I'd consider them good friends at that time. They like each other, they respect each other, they trust each other (both having earned that trust), and they care for each other. Can you follow so far?
Why is Claire the right woman for him? I think it's for the same reason he's the right man for her: because he has experienced that, around her, he can just be himself. Faye used to beat him when he wasn't careful; Dora used to flip out when he looked the wrong way or said something stupid, he cannot even be open to Steve about certain issues without being mocked. Claire has a sharp wit (and I don't mean the puns), but - unlike everyone else in his life - she never makes fun of him.
So it starts with feeling comfortable around each other. Then you miss her, when she's not there. And slowly you start to realize that there are feelings, that you cannot ignore them, and that you want to act on them. It's a slow process (especially with Marten's usual processing speed), which is why it's difficult to point to a single comic and say: "There it began!". If you've never had it happen to you, it may be difficult to understand. But it happens.