Yep, bounty is awarded when that player's ships/structures/planets are destroyed. When you place a bounty, it's distributed among all the player's assets, so if they're busy fighting it's easy to lose it.

Yep For the AI, when they have a bounty and you hover over their units, buildings, or planets, the info card will show how much bounty that specific unit is worth if destroyed. You can't see how much your units are worth, though.

You can't actually collect the bounty you placed yourself, only the bounty other players placed

The reason people say to place the bids at the end of the timer is so that the AI has less time to out-bid you. If you put it early, the AI has plenty of time to up the bid. At the end of the timer there's a short variable amount of time (up to 60 seconds I think) until the pirate raid launches, and that's what makes it the best time to place bids - not much time, making it much easier to win