Here are the answers to your questions:
Question 1: What is an absolute phrase?
Answer: a set of two or more words that includes a noun and a modifier and modifies a sentence.
Question 2: How is a phrase different from a clause?
Answer: A phrase lacks a subject and a verb.
Question 3: Which one shows how these sentences can be manipulated to create a compound sentence that has the same meaning as the original sentences?
Answer: Franklin spent an hour researching at the library last night, and he checked out four books to finish the project at home.
Question 4: What is needed to connect a dependent clause with an independent clause to form a complex sentence?
Answer: a subordinating conjunction.
If you have any more questions or need further assistance, feel free to ask!