No and yes, respectively.
Moving through an ally’s space does not require Squeezing. The space is difficult terrain, but opportunity attacks are only provoked by moving out of a hostile creature’s reach. So long as you end your movement without leaving goblin 1’s reach, you will not provoke an opportunity attack from it.
Once you are past the ally, you can make melee attacks on goblin 1. Since the fighter is another enemy of the goblin, is within 5 feet of the target, and is not incapacitated, you don’t need advantage on the attack roll to get sneak attack providing you don’t have disadvantage.