1) only if you change from android to iPhone (or otherwise). The purchase is linked with your Google or Apple account, you can use it with as much devices as you like, only a transfer between apple and Android is not possible.
2) yep, controler works fine with that game. (go to settings and controler setup, than you can set the buttons)
Edit: oh yes Alan has right. If you connect with the same account as purchased, go to store in main menu and click on restore purchase. Login first with the button top left in main menu