Yes this sentence can mean both "You can change your idea" and "You can change his idea". In order not to confuse them you can say
Kendi fikrini değiştirebilirsin for you can change your idea
Onun fikrini değiştirebilirsin for you can change his idea.
No, there is no such a rule. It's not the transitive verb that requires the accusative case in this sentence but it's the possessive ending in the object. You would always use the accusative case when you add a possessive suffix to an object.