Bots do shoot while in vehicles in minigames, but they don't seem able to operate Tank turrets or similar bot-weapons, and my memory's a little fuzzy on the matter. The bot
development thread has a full list of the Bot events available, and there is an
add-on available if you don't want to go through the trouble of eventing the bot not to do anything (though this only takes two events to do if I remember correctly.) Really, the best way to find out what bots can do is both to observe what's been done with 'em already and also to experiment.
On bots in the backseat again, I'm not sure if there's an event to make bots swap vehicle seats, and you'd also want to event the bot not to move, but only to attack (whom to attack is set via bot "teams", also default) in minigames.
Bot events right now are VERY flexible, but you need to learn and experiment with them to figure 'em out.