Glad you're thinking of experimenting with the electronics of OpenROV. As David has mentioned, the topic of power-over-tether has come up a number of times before- you should be able to find the old threads by searching through the forum.
I've looked in detail at doing this a number of times, and basically have never felt that it is worth the trouble. Your mileage may vary, especially if you have an application that requires you to be uninterrupted in the water for a very long period (say, over 4 hours). The high resistance of the tether causes large voltage swings with changes in load current, which must be dealt with on the receiving end- the ROV. You'll probably need some sort of switching power supply to convert the raw tether voltage to the battery buss voltage. That switcher will need to have some sort of maximum-power-point tracking to keep from pulling the voltage on the receiving end of the tether below the optimal point.
The documentation of the Controller Board is pretty minimal right now- basically just the schematics, Eagle design files, and the Gerbers which are posted on GitHub. I want to do a complete App Note for the board at some point- this would certainly help folks who want to tinker with bare board. Unfortunately, other projects keep getting in the way. So for the time being you're going to have to brush up on your schematic-reading skills.
As for your questions:
1. The board was designed to work with up to a 4S Lithium battery configuration, say 17 volts maximum. There's a TVS on the board that will soak up spikes over 20V (IIRC). If you want to put 24V on the battery buss, you're going to have to figure out for yourself which components are vulnerable.
2.) See above discussion.
2b.) Yes, the powerline (HomePlug) adapters work perfectly fine with a DC voltage on the output. We use a 5V signal riding on the HomePlug signal to turn the ROV on/off.
As for the mechanicals of the Controller Board, the board is 80mm by 150mm. There are 4 0.125" (3.175mm) diameter holes for mounting. The datum point for board measurements is the corner near which ESC3 is mounted. Referenced to this, the 4 hole locations are at (X,Y in mm) 3,3 27,77 147,3 and 147, 77
Hope this helps.