Will there be (A) another (B) artist as famously as (C) a pop star like (D) Justin Bieber?
C is incorrect. The correct phrase is "as famous as". "Famously" is an adverb, but we need an adjective to compare two nouns (artist and pop star).
Corrected: Will there be another artist as famous as a pop star like Justin Bieber?
Make (A) surely (B) to bring your student ID card with (C) you when borrowing (D) the books.
B is incorrect. "Surely" is an adverb. We need the verb "make" followed by an adjective. The correct word is "sure".
Corrected: Make sure to bring your student ID card with you when borrowing the books.
What are (A) the differences (B) from (C) a songwriter and (D) a composer?
B is incorrect. We use "between" when comparing two things.
Corrected: What are the differences between a songwriter and a composer?
They did not have any (A) rice in the jar, but (B) they had a (C) wheat instead (D).
C is incorrect. "Wheat" is an uncountable noun. We should use "some" or no article at all. Also, "instead" implies replacing something that was expected. A better word would be "flour" if they intended to make something with it. If they simply had wheat grains, then no article is needed.
Corrected: They did not have any rice in the jar, but they had some wheat (or wheat) instead. Or, if they had wheat flour: They did not have any rice in the jar, but they had some flour instead.
If you lose weight (A), will you be (B) as healthy like (C) a person who was (D) never fat?
C is incorrect. The correct comparison is "as healthy as".
Corrected: If you lose weight, will you be as healthy as a person who was never fat?