There's only one kind because heat recovery would require different technology. It's such a small amount so it doesn't matter.

Of course it's usable. First law of thermodynamics. It's basically electricity theft wether one does it directly or through induction. It's called a vampire drone for a very good reason.

Yes, inductively coupling to something increases the load on the primary (or any transformer would be a free energy generator). If it were using only the heat differential between the conductor and the air, like a Stirling engine, then no. In fact, if it acted to cool the powerline, it would probably increase efficiency, to a microscopic degree. And at that point, you'd get better performance from a solar panel.

However, inductively stealing a drone-portable battery on any practical time scale would be all but imperceptible on a powerline at 100kV carrying 500 amps (50MW).

If it's a UHVDC line (or any kind of DC), inductive coupling won't work at all.