#10 what is the adverb tomorrow modifying?

Adverbs modify, or describe, adjectives, verbs, and other adverbs.  When you read a sentence, you need to find the verb first.  In #10, would come is the verb phrase.  "Back" is an adverb describing "would come". Since you know the adverb is tomorrow, ask yourself, when are 'they' coming back?  They are coming back tomorrow, so tomorrow is modifying the adverb back.  That said, sometimes part of the verb phrase can go the other way, so you can say that it is modifying "come back".  As a teacher, I would accept both.  

what part do you need with?

adverb is the answer i believe.