RE: Prop balancing
Sanding the back side of the prop all along the edge and along the thickest part of the center of the prop (not the core but along a center line from the "center to the tip" will remove what you need to remove for proper balance. APC's are generally pretty good, and either don't require balancing or require very little. It won't hurt the prop.
If, though, it's really bad, then throw it away and replace it.
CGr.