In this sentence, the phrase "a man known for his pugnacious character" is acting as an interrupting phrase. An interrupting phrase is a group of words which interrupts the flow of the sentence; interrupting phrases need to be separated from the rest of the sentence with commas (or dashes). In this case commas are needed after "Patton," and after "character."

The full, correct version of this sentence reads: "Patton, a man known for his pugnacious character, was renowned for his generalship."

Here, the phrase "in many great novels" is acting as an introductory phrase for the rest of the sentence. In light of the fact that the rest of the sentence can stand on its own (grammatically speaking), this introductory phrase should be separated from the rest of the sentence by a comma, which, in this case, it is. The sentence has no grammatical errors.

The best way to correct the underlined portion of the sentence is to use a single comma and separate it from the remainder of the sentence. The phrase "unsure of how to proceed" here acts as an introductory phrase, and it should be separated from the independent clause with a comma.

The full, correct version of this sentence reads: "Unsure of how to proceed, he hesitated at the top of the pass."

Here the phrase "one of the greatest generals of all time" acts as an introductory phrase for the rest of the sentence. The clause provides a relevant contextual detail, but one that precedes the grammatically essential structure of the sentence, therefore a comma is need between "time" and the rest of the sentence.

The full, correct version of the sentence reads: "One of the greatest generals of all time, Alexander the Great had a nearly perfect military career."

Here, the phrase "the biggest jerk in school" is an interrupting phrase in the sentence. The phrase comes in to give us a description of John's personality, but does not affect the grammatically relevant portion of the sentence, "I really hated losing to john, but he simply outplayed me." "The biggest jerk in school" should therefore be separated from the rest of the sentence by commas. Also, since the coordinating conjunction "but" is used, a comma is required after "school" in order to prevent a run-on sentence.

The full, correct version of the sentence reads: "I really hated losing to John, the biggest jerk in school, but he simply outplayed me."

"One of the most challenging art forms," is here used as an interrupting phrase. It should therefore be separated from the rest of the sentence by commas. The author's opinion that acting is "one of the most challenging art forms" is descriptive, but not grammatically relevant to the fundamental subject-verb relationship of this sentence. The sentence could read: "Acting is my passion." 

The full, correct version of this sentence reads, "Acting, one of the most challenging art forms, is my passion."

Here, the phrase "my favorite food" is being used as an interrupting phrase, therefore it must be separated from the rest of the sentence with commas. "Cheese," the subject of the sentence, must be connected to the primary verb "is," so the interrupting phrase must be enclosed with commas, one on either end.

The full, correct version of the sentence reads: "Cheese, my favorite food, is the main reason I can never become a vegan."

Here, "in one form or another" is being used as an interrupting phrase in the sentence, therefore, it should be separated from the rest of the sentence by commas. The relevant grammatical structure of the sentence has "drums" (the subject) being used (the verb here is "are"). The additional phrase "in one form or another" interrupts the flow of the sentence to modify the universality of the statement.

The full, correct version of this sentence reads: "Drums, in one form or another, are used in nearly every kind of regional music on the planet." 

"Who had a great deal of experience working with all manner of students" here acts as an interrupting phrase, and, in this instance, is correctly separated from the rest of the sentence by commas. The sentence is correct as written.

Here, the phrase "a great man in his time" describes "Gaius Marius," and interrupts the grammatical flow of the sentence. It is therefore the interrupting phrase in the sentence, and should be separated from the rest of the sentence by commas. Note that in the example sentence the failure to correctly enclose the interrupting phrase with a second comma results in a comma use error, separating the subject from its verb.

The full, correct version of the sentence reads: "Gaius Marius, a great man in his time, was dismayed at what Rome had become."