Yes, eligible bachelorettes will be courted and sometimes married by rivals. I've never actually counted, but I think there's enough single ladies to go around the single lords - but the idea is to grab a good one with an extended, landowning family you can marry into. A girl with nought but a fiefless brother isn't much of a catch. I'm not sure if you get any tangible benefits from being in the family - i.e. better relations - but if there isn't, there ought to be.
Divorces don't happen in native. You can't steal someone's wife, only their fiancée; but you can dedicate a tournament win to a married lady, or occasionally fight duels for them if they're insulted, and gaining their favour has certain advantages.
If the monarchs have daughters you never see them, and if you ask a king about marrying into his family he won't like such a suggestion from an upstart vassal.