The sentence in which the adverb clause modifies an adjective is the second one - The veteran appeared proud as he saluted the flag.
The adjective here is <em>proud</em>, and the adverbial clause is <em>as he saluted the flag. </em>As you can see here, that clause is describing the adjective in more detail.
When did the veteran appear proud? - As he saluted the flag (it obviously modifies the word <em>proud</em>)
in that paragraph, the expression Mounting evidence could be a bit confusing, but it indicates that there's been reaserch about it before, and that it all points in the same direction, the more research proving the same point means the data is convincing. The answer is D.
Basically, this quote means that you should do what's best for you even if the choices you make might hurt someone else. It also states that you need to do things that are in your best interest, even if they hurt and are painful because at the end of the day you are the most important person and you deserve to be happy.
I would say that the best one is C