In which sentence is the underlined phrase an adverb clause?
a beagle puppy in the florida everglades was trained to sniff out pythons in the park.
although we might consider animals as pets, many animals work.

The sentence in which the underlined phrase is an adverb clause is the following one: Although we might consider animals as pets, many animals work.

Explanation:

Adverb clauses, also known as adverbial clauses, are dependent clauses that function as adverbs. Since they are dependent clauses, they must have a subordinating conjunction to link them to the rest of the sentence. In the sentence above, the adverb clause is "although we might consider animals as pets". It is an adverb clause of concession introduced by the subordinating conjunction although.

the sentence that avoid faulty coordination is:

culture, which is well represented in philadelphia, plays a major role including theatre, music, and the visual arts.  

faulty coordination occurs when the writer gives equal importance two different ideas (clauses) which in fact are not equivalent. in order to correct a misplaced clause or idea, the writer can place less important or emphatic ideas in a relative clause as in the previous sentence.