You know the difference between Complex and Compound correct?
Complex: A sentence consisting of at least one dependent clauses and at least two independent clauses
For example: “The expert who examined this scroll said that it was more than one thousand years old.”
Compound: A compound sentence is made up of two or more independent clauses, usually joined by a conjunction and, or, but, though.
For example: “I wanted to walk the dog, but it was raining.”
Having this knowledge in mind you have to realize that complex is not the correct answer. Compound is the correct answer.
2. Dangling modifier is the error in the sentence.
3. Most of the teachers are Americans, though a few came from England and France. Main clause: Most of the teachers are Americans. Subordinate clause type: Adverb
4. You must remember that a modifier is a word, phrase, or clause which functions as an adjective or an adverb to describe a word or make its meaning more specific. The one mentioned above, for example is: pick. You are definitely correct.