A dependent clause is a chunk of a sentence that is almost a full thought, but relies on more information to become a full sentence.
So for this sentence, "that are more serious and suspenseful" is a thought that almost makes sense on its own, but does not quite make sense without some more information.
The only relative adverbs that exist in the English language are when, where, and why. So I'm not sure what you mean when you ask for a relative adverb, because there are no relative adverbs in that sentence.
