I would wire them together in a parellel circut. all the lights together, white to white black to black then put your ballast to em. it works like that with my 400 watt mh/hps ballast and 2 250 watt hps bulbs. run 2 hps bulbs with 2 mh bulbs if you can, you get better results.
If you mean the ballast in a fluorescent light fitting where the ballast is wired in series with the tube, the answer is "No". Explanation: If no tube is in place, the light fitting's circuit is "open" so there is nothing to take any current from the "hot" supply wire and return it to the "neutral" wire.
The white wire on the supply side. There isn't a common on the output side of the ballast.
Turn off the power, remove the bulbs, and remove the cover to expose the ballast. If you see tar leaking from the ballast it is bad and must be replaced. If you see no tar then proceed. Use a multimeter to check for continuity. The yellow and blue wires are the power wires and the white wire is neutral. With the meter set to ohms check between the yellow wire and white wire at the end where it connects to the light. If you get no reading the ballast is bad. Now check the other side where power is coming in. No reading and the ballast is bad. If you get a reading at both ends it is good. Check for loose wires.
no
not unless the wire is exceptionally small, if if is 12 AWG or even 14 AWG you will be ok unless you are using it for a transmission line (unlikely) The smallest wire you can use safely is a 21 AWG wire but that's not a wire used in the walls
No, not a good idea. You have to use a 347 volt ballast.
Modern light bulbs are made of tungsten wire.
Connect them in parallel. The black wire from the ballast to the black line wire. The white wire from the ballast to the line neutral. Connect the ground wire to the ground screw which is located in the body of the fixture. Grounding of the fixtures is essential.
I was told that the ballast resister is a twisted wire within the distributor cap area.
You don't. A ballast with a 347 volt input is a commercial ballast. The 347 volts comes from a 600 volt three phase four wire Y system. You can change the ballast out to a 120 volt and rewire the unit but in most cases it is cheaper to buy a completely new lighting fixture.
Yes, but it will not work.
Cap the extra wire with the appropriate size wire nut so that it will not short out against grounded objects.