The sentence that correctly identifies an adjective phrase is sentence C.
Explanation:
The adjective phrase in the sentence above is the following one: Who won the election. This is a restrictive adjective phrase as it helps identify the noun it refers to. If it was dropped, the meaning of the sentence would be changed (see 1). As you can see, the meaning of the sentence is different without the restrictive adjective clause.
In terms of the first question, "They" would be an objective pronoun, but it should be noted that this does not have to be so. for the second, the answer is "my".
