Option A correctly uses "children's" for a possessive plural, "its" as a possessive pronoun, and "who's" as a contraction for "who is." Option B incorrectly uses "Its" instead of "It's" (it is) and "it's" instead of "its" (possessive). Option C incorrectly uses "peoples'" instead of "people's" for plural possessive, and "teams'" should be "team's" for singular possessive. Option D incorrectly uses "sister's" instead of "sisters'" for plural possessive, "its" instead of "it's" (it is), and "who's" instead of "whose" (possessive).

Option A correctly uses a comma before the coordinating conjunction "but" to separate two independent clauses ("She wanted to go to the concert" and "she had to finish her report first"). Option B is incorrect because a comma is needed before "and" when it connects two independent clauses. Option C is incorrect because "did not like writing essays" is a compound predicate sharing the subject "He," not a separate independent clause, so no comma is needed before "but." Option D is a comma splice; two independent clauses cannot be joined by only a comma without a coordinating conjunction or a semicolon.

Option A correctly uses two commas to set off the nonessential appositive phrase "an avid cyclist," which provides additional, but not essential, information about "My brother." Option B is incorrect because it is missing the closing comma after "world" to fully enclose the nonessential appositive phrase. Option C is incorrect because it is missing both commas needed to set off the nonessential appositive phrase "a talented artist." Option D is incorrect because "that I borrowed from the library" is a restrictive clause, essential to identify which book, and therefore should not be set off by commas.

Option B correctly places a comma after the introductory prepositional phrase "Because of the heavy snow," separating it from the main clause. Options A and C are incorrect because they omit the necessary comma after their introductory phrases ("After a long and arduous journey" and "Having completed the assignment"). Option D is incorrect because the comma is improperly placed within the introductory phrase "Despite, the bad weather conditions" instead of at its end.

Option D is correct: "sister's" correctly shows possession, "its" is the correct possessive pronoun without an apostrophe, and "it's" is the correct contraction for "it is." Option A is incorrect: "Its" should be "It's" (it is), and "it's" should be "its" (possessive pronoun). Option B is incorrect: "childrens'" should be "children's" to form the possessive of the irregular plural noun "children." Option C is incorrect: "Who's" should be "Whose" (possessive pronoun), and "teams" should be "team's" (possessive noun).