In a 2-investigator game, if he rolls 3 successes, does the remaining success get accumulated toward the next doom token removal? Along the same vein, if he rolls 4 successes, does he remove 2 tokens?
Yes, left over success rolls do carry over, but the number of success required depend on the GOO that you are facing and the number of players. Also, if the GOO awakens, you always fill up the doom track if it wasn't already full.
The following is quote from the FAQ which you can find on the FFG Arkham Horror website:
To defeat the Ancient One, the players must do a total number of successes equal to the number of players multiplied by the number of doom tokens on the Ancient One. So, if 4 players are facing Yig (doom track of 10), they need 40 successes to win. For every 4 successes they do, they remove 1 doom token to track their progress. If the 12 investigators get 9 successes in the first round of combat, they would remove 2 doom tokens, and 1 success would carry over to the next round of combat.