Answers,
1. YES, without a doubt, and it's getting much more common, not just ford but so called prestige marks like BMW also.
2. Yes it will get really hot, it turns the excess voltage into heat, when it resists it, like if Cheryl Cole was trying to rip my clothes off I'd get hot resisting her, so wouldn't ha ha!!
Bypassing the overheat diode is safe enough, so long as fuses in place, and diode is not anywhere it could do damage from heat etc.
3. You can test before fitting another resistor, but don't pay for it, yours is faulty so return it.
tabetha