Thought Sponge checks how many cards were drawn by opponents this turn, even opponents who have left the game. The greatest number drawn by a single opponent is how many +1/+1 counters it enters with.

Thought Sponge checks the total number of cards drawn by each opponent, not how many were drawn due to a single instruction.

Use Thought Sponge's power as it last existed on the battlefield to determine how many cards to draw for its last ability. If that number is negative, you neither draw nor discard cards.

Thought Sponge gets its +1/+1 counters at the moment it enters the battlefield. There's not a time that it's on the battlefield before its replacement effect has applied.