I would certainly be using solid copper RG6 for over 500 feet or so, RG11 over 1200 feet or so, and more likely be considering fiber for the video for those distances.
If I were going to provide remote power, I would probably use tray cable. It is available in 18 gage and larger, it is designed for direct burial and also has an overall shield. You may want to upsize the wire from what is originally recommended to compensate for the voltage drop for those longer distances. Although I don't see any technical reason you couldnt use solid conductor, it would likely be easier to handle the stranded wire in conduit.
There should be no problem running the two in the same conduit.
Good Luck! It is only my opinion, based on my experience and education...I am always willing to learn, educate me!
Daron J. Wilson, RCDD
daron.wilson@lhmorris.com