For #2 of the Gravity part of the AP style problem, I'm not sure why speed has to increase in order to increase the radius. I thought speed has to decrease because of the inverse relationship with radius according to the derived equation, v = square root of Gm/r.

That is a FANTASTIC question, and to answer it, we need to understand that by accelerating at the top position, we're no longer maintaining a circular orbit, but setting up an elliptical orbit.  If we increase the speed of the satellite in that top position, we've increased the kinetic energy of the satellite at that position.  But a more complete orbital analysis must take into account gravitational potential energy.  By increasing the kinetic energy at the top position, we'll trade that speed off for gravitational potential energy at the bottom position.  The following web page goes into more detail (https://www.physicsforums.com/threads/orbital-speed-faster-is-closer.733175/), but the best way I've found to get a good feel for orbital mechanics is to play games.  As mentioned on the thread above, Orbiter is a free game that will give you a good feel for it, but Kerbal Space Program is a lot more fun in my opinion (though it's not free).  :-)