Question

I have to identify the adverb, what is modifies, and identify if the modified word is an adverb, adjective, or verb.

They work very carefully when they are up in the tops of trees.

Adverb very describes adverb carefully?
adverb carefully describes verb work?

and.

They became professionals when they were only 17 and 16.

adverb is only that modifies ?

Answer 1

Your first answers are right.

The second question is tricky. The adjective "only" modifies 16 and 17.

http://dictionary.reference.com/browse/only

Answer 2

What about these two?

The two teenagers climb high in order to cut branches that might suddenly fall on a house or a wire.

adverb suddenly describes fall verb
high describes climb verb

and

They were once called in the middle of the night to remove a tree that had fallen dangerously close to a house.

adverb once describes called verb
adverb dangerously describes close adjective?
adverb dangerously describes