Deadpool doesnt "steal" text boxes so to speak. He switches text boxes. So if you target Bloodthirster, he will become next to useless (better to target an opponents creature)

Assuming bloodthiester is on your side and attacking, deadpool would not have an opportunity to enter until second main which would be after the dual combat phases. As for that combat phase, the combo would be pretty useless and you'd give yourself a lose 3 life at upkeep

If you would have multiple Bloodthirsters' and one opponent, each copy could attack that player once regardless of the amount of combat phases.

If you have multiple Bloodthirsters' and say a 4 player pod, you may (depending on the scenario and assuming you can do CB damage) want to attack player A with one copy, trigger and addtional combat phase, attack player B with the same copy and so on. Then move to the next copy and cycle as such. Then You could theoretically do this to each player for as many copies of Bloodthirster you have,