Depends, are you a cop?

It would probably be legal.

How do you think they catch grow-houses? They thermal scan neighborhoods for heat signatures from the grow lights. Cops are masters of subverting the law to do whatever they want.

I know thermal imaging has been used to look for marijuana farms, back when grow lamps were incandescent and houses would stand out as hot. But I don't know if they had warrants for those or not.

But to actually use imaging, whether it's thermal, radio, or X-ray, to see through a wall, is definitely considered a search.

Thermal cameras can't see through glass, but they could be used to see if a building is significantly warmer than the surrounding structures.

https://en.wikipedia.org/wiki/Aerial_surveillance_doctrine

That's a good place to start. It summarizes a few supreme court cases that you can read more about.

This is not correct. Navigable airspace is controlled by the FAA alone. Part 107 rules state that in fact you must fly a small unmanned aircraft less than 400 feet above ground level or within 400 feet of a structure. So, if someone is flying a drone around, they must fly it fairly close to the ground (though a little quadcopter at 400 feet would be pretty hard to notice).

If a police aircraft gets shot down, they're just going to arrest everyone they can find nearby and work it out from there.

That's what they do when a police helicopter gets hit with a laser pointer, I would assume it would be the same in this case.