You put only one +1/+1 counter on Thoughtbound Phantasm each time you surveil, no matter how many cards you looked at when you surveilled.

Once Thoughtbound Phantasm has attacked, removing +1/+1 counters from it won't remove it from combat.

An ability that triggers "whenever you surveil" triggers after you're done surveilling, even if you have fewer cards in your library than the number of cards you're instructed to surveil. It even triggers if you have no cards in your library.