What is the source of the vibrations apparent the FFT
First, I find the 3D waterfall style plots pretty hard to interpret. My preferred method is a 2D color map (e.g. pcolor() in matlab).  It's a lot easier to see your frequencies.  

To your first question, it's going to be hard to answer that without knowing a lot more about your system.  Vibration at twice gear mesh frequency is certainly possible.  It's also possible that you have a structural mode.  The first thing to do to investigate this is to do a frequency sweep of your drive speed. Look to see whether this higher frequency tracks with the drive speed.  If it is synchronous with the drive speed, then you know it is definitely related to something rotating.  

Your second question is essentially impossible to answer without knowing a ton more information about your system.  e.g. what kind of motor is it?  permanent magnet DC? 3 phase AC induction?  How are you controlling it?  Is there any load on the gearbox or is it spinning freely?  You'd probably need to post all of the electric schematics, pictures of the entire setup, and more data.  I doubt it's the kind of question that would be easily answered on this kind of forum.