The correct answers are Who are you going out with?, With whom are you going out?, and What restaurant are you going to?.

In English questions, prepositions usually go at the very end of the sentence in informal and standard speech (e.g., Who are you going out with?).

In highly formal speech, the preposition can move to the front of the question word (e.g., With whom are you going out?).

You cannot double up the object ("with him") when the question word ("Who") already serves that purpose, and you cannot simply drop the required preposition ("going to").