1. I'm not sure, it's nearly impossible I think.
I use the 12's gauge, but only comfortable to play in drop C to standard tuning.

2. I don't think it has anyting to do with the nut, and your guitar doesn't have a floyd-rose tremolo, so the only thing you may have to adjust is the action and truss-rod, especially if you're going to tune to standar tuning with heavy gauge.

CMIIW