I have always had "bleed through" of my game screen which activates whatever is behind my game. For instance, when scrolling the in-game menu with my mouse or while using my controller I see my desktop icons highlighting as my mouse passes over them even though I'm actually in the game. Nothing actually opens behind my game screen but definitely becomes activated as the in-game cursor passes over it. I hope you can make sense of that.
As for the incorrect scores for a returning player, this is a long standing bug for TGC2 that has been complained about forever! HB has shown no interest in correcting the issue in the past and I highly doubt they will change their thoughts on this now either.
As for the issue where you see your opponent up to hit while he is seeing you up to hit, there is no need to leave the game to fix this. Simply uncheck your turn order box, take your shot and turn turn order it back on again by rechecking the box. You should be back in sync again after this and see each other in proper order once again.