A "duel” is a fight that adheres to a specific set of rules, while “dual” means having the quality of two. So, "duel" is being incorrectly used in this sentence, and to correct the sentence's error, you would need to replace "duel" with "dual."

"Their" is a possessive pronoun that means "belonging to them," but nothing is being possessed by anyone here; the flavors do not belong to anyone in this sentence. "There" would be more appropriate.

“They’re” is used to abbreviate the phrase “they are,” while “their” is used to show possession.  Since possession is being shown, “their” should be used, not “they’re.”

“Lead” is the present tense form of the verb “to lead” for a plural noun. However, the appropriate form of the verb for the singular subject (Sarah) in the past tense is “led.”

"Your" is a possessive pronoun. It should be replaced in the sentence with the contraction for "you are," which is "you're."

"Weather or not you like stormy whether" contains the sentence's errors. "Weather" is a noun that means atmospheric phenomena like rain, snow, or sleet, and "whether" is a conjunction that presents two options, as in the sentence, "I couldn't decide whether or not to wear my heavy coat that day, because the weather was supposed to start off freezing warm up drastically." So, to correct this sentence's errors, "weather" and "whether" should be switched around, resulting in the sentence, "Whether or not you like stormy weather, I enjoy listening to the thunder, watching the lightning, and hearing the rain plunking against my house's tin roof."

To answer this question correctly, you must understand the distinction between the homonyms "then" and "than." "Then" refers to an event that happens after something, as in the sentence, "He came home from work and then watched television." "Than" compares two words or phrases, as in the sentence, "I like chocolate chip cookies more than peanut butter cookies."  So, "than" is the correct word to use in this situation, and "then" should be changed to "than" to correct the sentence's error.

The sentence uses "there" incorrectly. This is an easy mistake to look over since "there," "their," and "they're" are all homonyms—words that sound the same but have different meanings. The speeches politicians make about the issue belong to the politicians, so the proper form is "their," the possessive pronoun.

The key here is to distinguish between the homonyms "your" and "you're." 

"Your" is a possessive pronoun identifying something that belongs to you. The first usage here is correct because "your mother" refers to the mother that belongs to you.

"You're" is a contraction that combines "you" and "are," and this would be the correct choice for the second usage, making the corrected sentence "Your mother's signature cookie recipe is incredibly delicious, and I'm incredibly jealous that you're lucky enough to enjoy those sweet treats whenever you want them!"

This is an incorrect form of the word "its." Here, the sentence uses the possessive pronoun form of "its," but there is nothing being possessed here. Instead, this sentence needs to use "it's," the contracted form of "it is," to be grammatically correct.  The corrected sentence reads, "Even though it's only February, I am already excited for summer break and warmer weather."