Learn Turkish: Bayat balık bulantıya sebep olmuş olabilir. - Stale fish might have caused the nausea.

The main verb is sebep olmak (to cause). To express a guess about a past event ("might have done"), Turkish uses the reported past suffix -mIş on the main verb, followed by the auxiliary olabilir (it can be / it is possible). So sebep olmuş olabilir essentially means "it is possible that it caused."

What is the difference between saying sebep olmuş olabilir and sebep olabilirdi here?

sebep olmuş olabilir means "it might have caused" (it is a real possibility that it happened). sebep olabilirdi means "it could have caused" (a hypothetical past possibility, implying it actually didn't happen). Since we are guessing the real cause of the nausea, -mIş olabilir is the correct choice.

Why is there a -ya ending on bulantıya?

The verb sebep olmak (to cause / to be a reason for) requires the dative case (-(y)a/-(y)e) for the thing being caused. You can think of it as being a reason to the nausea, so bulantı (nausea) becomes bulantıya.

What kinds of food does bayat describe?