A lot of people have answered your 1st q. Regarding the 2nd q (something I do to add word count), you should add those two quotes if possible in the same sentence because it's arguing the same statement.
I'm treating it as the rocket being launched infinitely far away (as r increases) and so, kinetic energy (ie it is decreasing) should be inputted to give the rocket its gravitational potential energy (ie which is increasing) by the conservation of energy.
You are correct (: Essentially, cooper pairs move around as a large loop of current near the surface of the superconductor, called a meissner surface current, and this current loop creates its own magnetic field that completely expels all the external flux of the magnet from the interior of the...
1. They are meissner surface currents, not eddy currents.
2. No, maglev trains have nothing to do with meissner effect. The EDS (electrodynamic suspension) maglev trains utilise superconducting electromagnets to create REALLY STRONG magnetic fields which allow it to levitate.