Solar powered routers and security cameras
There are a few issues you will have to overcome here, and most are solved much more easily by running cable. 


Solar power has limitations. For example, in Scotland I would need a pretty big solar panel to power the camera, wireless router, and charge a battery (for night time) and for many days of the year I wouldn't be able to get any charge (sunshine at 57 degrees north is minimal in winter!) but if you live in California or Arizona etc you may have much better luck with this.
Wifi extenders are cheap and convenient these days, and again, you can power them from solar panels, with the same caveat as before.
Directional antennas are a much better idea than a wifi extender, however. They will easily increase your wifi range, and have the added benefit of suffering less interference from any signal off the main lobe, and potentially increase security, as an attacker will need to be much closer if they aren't on that lobe direction.


I used to build a lot of setups with directional antennas for anything from a couple of hundred feet to a mile or so. Even at 100mW transmit strength, directional Huber-Suhner patch antennas gave me sufficient signal strength.

I'd still suggest a cable for the job you describe, though, possibly just run PoE (Power over Ethernet) so only one cable set needed.