1. No, because the power has already been transmitted. There would be problems if there were billions of these devices around a transmitter, because that would affect the loading. But one isn't going to make a difference.

2. Potentially yes, but the actual shadow is tiny. And transmitter powers are fixed and limited anyway.

3. Yes, of course. So is any form of undirected radio transmission.

4. This actually works. Kind of. You need to run the line parallel or build a resonant mix of L and C at 60Hz (or 50Hz.) You can also do things like power fluorescent tubes by induction.

https://www.trendhunter.com/trends/magnetic-field-fluorescen...

The problem is the voltage/current is very hard to control, and the whole point of electric fences is that they're not lethal. You'll get something out of a resonant circuit, but if you're not a qualified electrical engineer it won't be the clean 110/60 or 220/50 needed for an electric fence.