On 1: You consider a foundation in Math, and selected core Physics courses
On 2: You could consider a Master program in Physics. You may need additional core courses as well.
On 3: You might try an internship at JPL while completing your doctorate.
PS
It ain't easy but many of your class...
Lots of good reasons. You probably already know the design practice dates back to one of the earliest uses for the semi-conductor. With some caveats, using discrete transistors (or packaged arrays) as switches can speed up circuit switching speeds (PIN Diode switches for example), reduce circuit...