Question

2.Allen stayed out until midnight. Although he had promised his parents he wouldn’t. sentence or fragment

Answer 1

Well, the sentence is a complete sentence with a subject and a verb. The second clause, which has a subject and a verb, (he / had promised) isn't complete because you expect something else when you read it. The word although, a subordinating conjunction, makes the reader what happened in spite of promising his parents he wouldn't.

You could combine the two to make it a complex sentence. Although he had promised his parents he wouldn't, Allen stayed out all night. Now it is clear what happened in spite of his promise to his parents.