why ıs the 4th orange is mıne just portakal and I am eating the 4th apple elmayı... is it because there is an action taking place.
In this sentence, "The 4th orange" is the subject. Subjects never get the accusative case. Only objects do. :)
Could it also be "yours is the fourth orange"?
Yes, it could be. Though, I would translate the sentences as straightforward as possible, otherwise there will be millions of alternatives :)
Is he a fan of Arsenal?