Print out the posting and go to your favorite auto parts store. All the parts are generic and the people there can help you find it. If you know a friend that is good with electrics, enlist their help. This isn't something that a person with no electrical knowledge should tackle.
I would assume the coil of the relay would have the resistance equivalent to the original bulbs. I doubt 10 watt resistors would get very hot used as they will be, and are probably overkill. I used a similar setup on my Land Rover for my 4 off-road driving lights, and never used a resistor on the coil.
The resistor has to go in series with the head light power and that feeds the ballast input. If that's the way you are doing it, which does not require the relay. If you ar using the relay you don't need the resistor. The head light power connects to the relay coil. 12 volts from the battery goes to one side of the relay contacts and the other goes to the ballast.
The TIPM monitors all of the electrical components of the car. If the current draws isn't within what it expects it to be, it will try to correct the condition by turning the circuit on and off. Eventually, if the problem doesn't clear, it turns the circuit off permanently, and requires a reset. Most times that requires a visit to the dealer.
I don't know from what you have posted as to how you have the HIDs connected electrically. If you have the relay connected properly, the HIDs shouldn't flicker. The HIDs should be getting their power directly from the battery via the relay. Unless you can better describe what you have done, I can't help you. If you're not good with electrics, I suggest you enlist the aid of someone you know that does.
Just as I instructed in my original post, one that they sell at auto parts stores for add on lights. Should be an SPST.
