Learn German: Ihr tut nichts gegen das Problem. - You are doing nothing against the problem.

Yes, gegen is a preposition that always forces the accusative case! However, for neuter nouns like das Problem, the accusative word for "the" is exactly the same as the basic subject word: das. If it were a masculine noun instead, you would see a change (for example, gegen den Mann).

Who is Ihr in this sentence?

Ihr is the informal plural "you" (like saying "you guys" or "y'all"). You use it when you are talking directly to two or more people whom you would address individually as du.

Could I say macht instead of tut?

Yes! The verbs tun and machen both mean "to do" or "to make." Saying Ihr macht nichts gegen das Problem is perfectly natural and means the exact same thing. Tun is often used in phrases about doing "something" or "nothing."

What is the difference between nichts and nicht?

Nicht means "not," which is used to simply make a sentence negative. Nichts with an "s" at the end means "nothing." Here, you are literally saying "You do nothing against the problem."