[Coda]

There are way more kinds of energy than just kinetic and potential. Electrical energy can do work too (motors!) and heat is a form of energy that isn't doing work. But yes, for these basic mechanics questions, kinetic and potential are the only ones you're going to be concerned with.

"Transfer of energy" isn't jargon; it's not a piece of scientific vocabulary that always has to be used a certain way or you're wrong. When I say that, I really just mean that energy is moving from one place to another, or from one state to another. (Converting potential energy to kinetic is work, done by the force of gravity.)

It sounds like you've basically got everything straight here.