As per your questions:
1) The relay that comes with the HID kit enables you to power the ballasts directly from the battery to ensure the ballasts always receive a constant 12V. With this harness installed all you end up using your vehicle's OEM headlight harness for is simply to trigger the relay in our harness on/off.
2) Your lights will function exactly as stock with the HID kit installed.
3) Xtreme ballasts are low draw meaning that you can safely power them directly from your OEM headlight wiring with or without the relay harness.
4) This kit will not run any hotter than your halogen bulbs.
5) XenonDepot HID Kits
come with proper mating connectors. You will not get generic spade terminals that require you to secure them with electrical tape (common with other HID kits).
Hope this helps!