I think wherever there is an "or", the reverse order should also be accepted ("Is that Finnish or Estonian?" in this case), because it means the same thing.
Languages are always partitive
Why is "-a" ending necessary here? It means some like indication, "is that thing we have just heard estonian"?
Because you haven't heard the entirety of the language, just some utterances in it.
I'm not noticing a distinctive intonation that indicates a question is being asked. Is this something that is not done in Finnish?
In Finnish there's no rising intonation in questions.