This sentence contains no errors. The words "to" and "after" both start prepositional phrases, meaning that they are a part of the main clause as well. No additional punctuation is necessary: commas are used to separate clauses (there is only one) and colons combine clauses when the second one explains or clarifies the first (again, only one clause). The correct choice is, "He planned to retire to the mountains after this year."

This sentence contains no errors: it is a simple sentence. Note that prepositions (e.g. "since") do not mark the beginning of a new clause, but simply a prepositional phrase - they are still considered a part of the same clause as the words preceding it. Additionally, commas are generally used to separate clauses (as stated before, there is only one clause). No changes should be made. The correct choice is, "She has played the guitar ever since she was very little."

This sentence contains no errors. The sentence combines two related independent clauses without the use of a conjunction, so a semicolon is appropriate after the word "poetry." Additionally, "though his poems were short and sweet" 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. The correct choice is, "himself in his poetry; though his poems were short and sweet, they contained much gravitas."

This sentence contains no errors. The words "large" and "strong" are coordinate adjectives describing the word "foundation." These adjectives 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 large, strong foundation was necessary for a building."

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."