Tools for installing splitfaced stone sheets (mosaic-like) on a wall
Trowel - This depends on your substrate.  If I am going on perfect straight backer board I might go 1/8", for drywall or not perfect go with 1/4".

You should notch horizontally.  Actually it doesn't matter if you do it right but horizontal will help them from falling initially.

Nippers... No way.  You will need a wet saw or angle grinder with diamond blade.  You will need to take the sheets apart and cut each piece individually unless you have a really good wet saw with a good feeding track.  

If you are waiting for a backsplash to come in, I suggest you install that first.  You should start this tile right next to the backsplash and work your way out.  Always start at the focal point and know that you can hide bad cuts in corners.  

To hold tile up during install... we usually use 2x4s.  But really if your mix is right and you trowel right these tiles will hold up just fine.  You would do the bottom row first and just make sure you give the second row 20-30 minutes before you start stacking.  But if you want to put something under that is fine, but you shouldn't need to.