Lots of used units on ebay. Just make sure you get the right part number. Xenons come in two type. Remove the headlight and check the part number. Careful not to buy halogen only. New units are available for like 1400$ for both left and right last time I checked. New from vw are like 900$ each side.
Remove all of the insulation from an individual wire that had not already fallen off;
Cut that wire in two;
Re-insulated each half with heat-shrink and shrunk it down;
Fed a 25mm piece of heat-shrink on one half;
Crimp the both halves together using crimps used for crimping fishing wire traces using the smallest crimps you can find for the wire size;
Fed the 25mm piece of heat-shrink over the crimp;
Shrink the heatshrink over the crimp.
Electrical tape are heat resistant, usually to around 100C. The Hid Bulb will surely get hotter than that, but the bulb it self is inserted into the housing which is insulated. The wiring is behind this and well separated between the source of heat and the wiring. It is unlikely the temperature at the wiring will exceed 100C, so using electrical tape will probably be fine. That being said, I've used electrical tape to tape up frayed wiring and it's held up for the past few years with no sign of wear or degrading yet.