When I got married, I thought about this a little, and I concluded that marriage (but not cohabitation) would:
Create a partner with a non-betrayal stance towards me (i.e. would not defect against me in a one-shot Prisoner's dilemma game).
Signal to others that I and partner had a non-betrayal stance towards each other.
It's an interesting question why marriage is able to create that first effect, and I don't have a good answer. I do think that many people go into marriage without thinking of these considerations, and I think that is a mistake. In other words, I think that the answer to your third question is no. But that depends on society's tolerance of cohabitation, which wasn't always society's attitude.
It's an interesting question why marriage is able to create that first effect, and I don't have a good answer.
I can think this is because it is an act that is supposed to entail the following:
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.