Learn Spanish (Latin America): No estamos para bromear sobre el problema. - We are not in the mood to joke about the problem.

The phrase estar para followed by an infinitive like bromear or a noun is used to express whether someone is in the right mood, mindset, or condition for something. Saying no estamos para bromear translates well to "we are not in the mood to joke" or "this is not the time for jokes."

Could I use por instead of para in this sentence?

That would change the meaning completely. While estar para expresses your mood or readiness for something, estar por followed by an infinitive usually means "to be about to" do something or "to be in favor of" it.

Is there a difference between saying no estamos para bromear and no tenemos ganas de bromear?

They are very similar, but no estamos para often carries a slightly heavier, more circumstantial tone. While no tenemos ganas simply means "we don't feel like it," no estamos para implies that your current state of mind or the gravity of the situation makes you unready or unwilling to joke.

Why use sobre el problema instead of del problema?

Both are correct and natural. The preposition de can easily mean "about," so bromear del problema works just fine. Using sobre is simply a more specific way to say "about" or "on the topic of" the problem, which emphasizes that the problem is the subject of the jokes.