Of the desert is the prepositional phrase
Afterward is the correct answer
No it is not. It is an adverb phrase since it lacks a subordinating conjunction.
Adverb clauses must be preceded or started by a subordinating conjunction such as after, if, because or although. For a sentence to qualify as an adverb clause it must include in its body a subject and a verb.
As a general rule you can use the following formula:
An adverb clause equals a subordinate conjunction plus a subject plus a verb, and it should be answering how? when? where? or why?
The lines which are a flashback here are: She thought of her last day in middle school, seven years ago, when Sarah had given her an iPod. She had felt ecstatic that day when she realized she would be able to listen to her favorite songs and fend off comments from her cousins about how little she knew about music.
Reading because she loves the books a lot