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1) As you mentioned, tap into the rear back up light for the camera power.
2) For the monitor power, get a fuse tap, and use a fuse in the passenger footwell that will be only powered when you start the car.
3) Both the inside car Receiver and the monitor positive (red) wires will use the same fuse tap.
Find a place to put the negative (black) wires for the transmitter and the monitor power source cable.
Once this is wired, then once you have the car running, and put it reverse, the camera will power up from the BU lights, and the monitor and receiver will already be powered and will turn on with the camera transmission.
I powered my back up camera, with ALL power wires coming of the reverse backup lights. That way both the screen and the camera ONLY comes on when in reverse. Very low voltage needed, so it doesn't affect anything. You can use a fuse if you wish, on the positive wire where you connect it to the bulb wires, but that's already fused as well, in the fuse box.
I installed a piece of bent metal into my air vent, and holds my camera. No wires showing, no interference with doors or anything else in the car. Works perfectly.