The fragment and the sentence can be joined together with a simple comma to make one complete sentence.

Because all three of these sentences can stand independently by themselves, separating the third with a semicolon keeps the new sentence from being a run-on.

Introducing the sentence with "even though" helps indicate that there is some contradiction between the two sentences.

The second sentence describes the dorm's location, so the following option is best because it allows the location as a description of the dorm:

"Maria was excited to move into her college dorm, which was conveniently located near her favorite campus quad." 

"Even though," "despite the fact that it," and "however" make it seem like the dorm's location is a negative detail, but the second sentence implies that this location is a positive detail through the use of the adverb "conveniently," so those options are incorrect.

The other option merely connects the second sentence to the first as a dependent clause that makes it sound as if Maria is "conveniently located near her favorite campus quad," so it is not as clear or grammatically sound as the "which was" option.

There are two grammatical errors in the underlined portion of the sentence. First, the two independent clauses need to be joined by the conjunction "and." Second, the two verb forms in the two clauses should be parallel, leaving "and wanted them to," as the only correct answer choice.

The answer choice "I should have stayed home from school today; because of this stomach virus, I am simply too sick to focus" combines two independent clauses with a semicolon, the second of which supports the first closely enough to merit the semicolon. 

Incorrect options:

"I should have stayed home from school today because of this stomach virus I am simply too sick to focus.": This answer choice is one sentence and a run-on.

"I should have stayed home from school today, because of this stomach virus, I am simply too sick to focus.": This answer choice combines two independent clauses with a comma, forming a run-on.

"I should have stayed home from school today, because of this stomach virus; and because I am simply too sick to focus.": This answer choice combines an independent and dependent clause with a semicolon, which you cannot do. The second part of the sentence is a fragment.

The underlined portion of the sentence contains an inappropriate use of the verb "overload." The use in the sentence needs to acknowledge the fact the final phrase is a fragment on its own. "Overloading" appropriately ties the phrase to the subject of "good ideas."

The use of the verb form "acted" makes the final part of the sentence an incomplete thought not connected to the first part of the sentence. The secondary clause must be joined with the main body of the sentence, either with a conjunction or a verb form that can connect the two. "Acting out each part based on extensive research," using the past participle, is the correct answer choice.

The relative pronoun “who” makes this sentence into a fragment, because there is no longer a predicate. The best answer simply removes “who.”

The sentence is written as a run-on sentence, as it is two complete thoughts not properly combined into a compound sentence. A compound sentence needs to have its two independent clauses joined by either a conjunction and a comma, or a semicolon. The only answer choice to employ either of these options is "The boy always gave his schoolwork his best shot, but he never could make himself into a good student."