Am I right in the problems below:

Although Rex behaves well, they take him to obedience class.

dependent clause is Although Rex behaves well and it is used as a noun?

He looks as if he wanted a good home.

dependent clause is as if he wanted a good home and it is used as an an adverb describing how he looks.

No, "Although Rex behaves well" is not a noun. The verb is "take". Who is doing the action here?

And, no, "as if he wanted a good home" is not an adverb. "looks" is a linking verb, therefore the phrase is a predicate adjective describing "he".

They are the ones doing the action so is it a noun?

For the next one my choices as noun adjective or adverb so would it be a noun or an adjective?

For the first one is it adjective and the second still just an adjective?

"They" is a pronoun, not a noun. It is the subject of the sentence. "Although" is a preposition, so you have a prepositional phrase describing Rex, or "him", the direct object of the sentence. Who is taken? Him. The phrase describes "him". What describes a noun or pronoun?

I don't see your multiple choice selections. An adjective is an adjective, in this case a predicate adjective, but still an adjective, not an adverb. It describes "he", the subject of the sentence.

Yes, you are correct in your analysis of the two sentences.

In the first sentence, "Although Rex behaves well" is a dependent clause because it cannot stand alone as a complete sentence. This clause is indeed being used as a noun in the sentence. More specifically, it is functioning as the subject of the sentence. The independent clause is "they take him to obedience class," which provides the main action of the sentence.

In the second sentence, "as if he wanted a good home" is also a dependent clause because it does not express a complete thought on its own. This clause is functioning as an adverbial clause, providing additional information about the verb "looks." It describes how he looks by expressing a condition or possibility. The independent clause in this sentence is "He looks," which is the main subject and verb of the sentence.