Learn Polish: Mogę zrobić cokolwiek, bo to jest spontaniczny wyjazd. - I can do anything, because this is a spontaneous trip.

Coś means "something," while cokolwiek means "anything" or "whatever." The suffix -kolwiek adds a strong sense of total indifference or unlimited choice. Here, the speaker isn't saying they can do a specific thing, but rather absolutely anything they want.

Is cokolwiek in the accusative case here? Does it decline?

Yes, it is the direct object of the verb, so it is in the accusative case. Just like the base word co, the accusative form of cokolwiek is exactly the same as its nominative (dictionary) form. If you needed another case, only the first part of the word changes while the suffix stays the same (for example, the instrumental case would be czymkolwiek).

Could I use the imperfective robić instead of the perfective zrobić here?

You could, but it changes the feel of the sentence slightly. The perfective zrobić (to get done / to complete) implies picking an action and accomplishing it. The imperfective robić focuses on the continuous process, which would sound more like "I can spend my time doing whatever."

Why use wyjazd for "trip" instead of podróż or wycieczka?

Wyjazd literally comes from the verb meaning "to drive out" or "to leave" and is the most common word for a standard weekend getaway, vacation, or trip out of town. Podróż is usually a longer, more significant journey, while wycieczka is typically a shorter excursion, hike, or guided tour.