The "AvailableMarkets" endpoint requires an event ID, but is the response always the same for every event from the same sport?

For every match you need to do the AvailableMarkets call to see which markets will be available in BetBuilder (OBB) for the match. The markets listed in the documentation are the ones available in OBB across all the supported sports, but that doesn't mean all of them will be offered for every match in these sports – AvailableMarkets providing you the list per match is the only 100%-reliable information.