This sentence contains no errors. The word "then" indicates a progression in time, whereas the word "than" indicates a comparison of things. The latter applies to this sentence (Additionally, a comparative adjective is used). The correct choice is, "faster than."

This sentence contain no errors. The word "their" is the possessive form of "they," which is exactly what is needed here. "They're" is a contraction for "they are." The correct choice is, "decided to play with their toys outside."

This sentence contains no errors. It is a simple sentence. Note that prepositions do not usually take any sort of punctuation preceeding them and never have punctuation between it and its object. The correct choice is, "resulted in some of the most miraculous paintings."

This sentence contains no errors. The phrase "which many thought was dangerous" is an example of a relative clause, which gives more information about its antecedent: the mission. Any such phrase that occurs in the middle of a sentence must be introduced and completed with a comma. The correct answer choice is, "mission, which many thought was dangerous, they made sure to check all of their equipment."

This sentence contains no errors. The phrase "while frustrating" is an example of an interjection, explaining the subject's feelings on the matter of "failure." Interjections are outside of the main clause, grammatically, and should be offset by commas on both ends of the phrase in order to separate them from the rest of the sentence. The correct choice is, "She believed that failure, while frustrating, was."

This sentence contains no errors. This is a simple sentence containing two prepositional phrases (starting with "as" and "of"). There is no need for punctuation anywhere in the sentence (and punctuation is never used to split up verb phrases). The correct choice is, "He decided to try meditation as a way."

This sentence contains no errors. The words "big" and "heavy are coordinate adjectives: adjectives that modify the same noun separately, but are not separated with a conjunction. Coordinate adjectives need to be separated with a comma. The correct answer choice is, "The big, heavy machine was necessary in order to complete."

This sentence contains no errors. The phrase "While looking through her scrapbook" is an example of an introductory phrase, explaining information necessary to the context of the sentence, but outside of the main sentence, grammatically. These types of phrases must be followed by a comma in order to separate them from the rest of the sentence. No other changes are necessary.The correct answer choice is, "through her scrapbook, she remembered many pleasant events from her life."

This sentence contains no errors. The word "dreamt" is a valid form of the word "dream." It is the simple past tense form of the word. No changes are necessary; the other choices only add unnecessary words. The correct choice is, "He dreamt of starting his own publishing."

This sentence contains no errors. The word "among" means in the presence of, specifically when whatever mentioned is not a group of things in general. "Between" is used when you have separate and individual things (e.g. between the two rocks). Note that "about" is not a synonym for "among." It means concerning/near. The correct choice is "among."