Considering the issues only started after you installed the H1 Xenons, I would start looking there. Making sure everything is connected properly and nothing is loose or half-way connected.
To me, it sounds like there could be a wiring issue, a grounding issue or something that is drawing the battery down.
Checking the battery it should be slightly above 12V when the car is OFF (engine off and nothing else on). It should also be above 14V (actually ~14.7V is a very good) when the car is ON (engine running). There is a "hidden" menu you can get to that should show you these voltages if you don't have a multimeter: