Question about winning conditions
 

Lets say for instance I use susano's effect to give my oppoment 1 battle reward. He now has 10. Do i have till the end of my turn to try and get 2 battle rewards or one to tie the game (or win, don't know), or does the game AUTOMATICALLY stop the moment 10 battle rewards has been reached?

brs are checked at the end of the turn, same with no cards being left in deck

Actually battle rewards are checked before someone decking out

but both are still checked at the end of the turn so what i said wasnt wrong

You also can't not tie due to battle rewards. In the case of both players having 10 or more brs on their respective opponents, attacker wins.