Are high level pokemons allowed to disobey and rebel against their trainers? 
What exactly defines a 'high level' Pokemon here? I'm not against that thought, but. . .
But also can pokemon be traded between players? 
Of course! 
 you don't have them badges to control me!
How do badges work? 
I didn't want to unnecessarily complicate this game, so as of yet I haven't implemented badges.