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You can't power the HID Ballasts off of the stock wiring for the headlights in which case you break up a circuit which counts on power flowing across the headlamp in order for other items to function accordingly. It is illegal in the US to operate fog lights while your high beams are in operation OR while the headlamps (low beams) are turned off. As such the system is built to only run them while the fogs are off. Also, because of the way the circuit is made other mods will affect the high beam functionality (including replacing the dash indicator lamp with a diode of any sort (LED)). So, you need to do some rewiring...

Power ballasts from the battery with fused relays triggered by the stock low beam wiring; I believe that you can trigger high beam ballasts via the stock wiring with relays without issue as well; Fog lights need to be rewired for independent operation (they can easily be rewired to remain legal versus fully independent if you like it's a matter of selecting the power source for the main fog light relay) and then again you'll wire the H3 ballasts to feed from the battery via fuse and relay and trigger that relay by the stock fog light output.

Oh and buy real H4 enclosures or you're just going to blind other traffic and attract police. Remember, blinded drivers actually tend to steer TOWARD the light. I recommend Cibie E-code housings then Hella E-code then Cibie or Hella DOT housings... in that order. eBay housings are nowhere on the list, they're shit... might as well just tape a few dozen flares to the hood, just as much light is going to actually make it to the road.