Welcome to the STD forum. Thanks for your question.
Before I even read the question, it is apparent from the title and your username that you are far more worried about HPV than most people are or anyone should be. HPV almost never is serious enough to be "consuming my life" or to warrant something like "please lord no".
You might have another conversation with your dermatologist about his confidence you have genital warts. It isn't always possible to accurately diagnose flat warts based only on visual inspection, and the location is a bit atypical; most genital warts involve the head and shaft of the penis (although pubic area lesions aren't rare).
Assuming the diagnosis is correct, the warts and the underlying HPV infection will clear up (and would have done so eventually even without freezing or other therapy). Although prolonged or recurrent infections occur from time to time, it's not the norm. Also, don't feel you have been singled out. At least 80-90% of all humans get genital HPV, often several times, and up to 20% develop warts as a result. Getting genital HPV is a normal, expected fact of being a sexually active person.
To your specific questions:
1) I would strongly urge your partner to have her third dose of Gardasil. She is probably partially protected by 2 doses, but it makes no sense to not go for complete protection. Because she has had 2 doses, though, and because Gardasil covers the two HPV types that cause 90% of genital warts, the odds are good she won't be infected, even if you have genital warts. She doesn't need to start over just becase the last dose will be late. Immunization is just as effective no matter when the last dose is given.
2,3) Yes, that's true. Without treatment, the wart-causing HPV types generally clear up in 6-12 months. It might be faster after treatment with freezing or other methods.
4) You need take no precautions with your current partner. She has been repeatedly exposued to what ever HPV strains you are carrying, and she is either immune to it (because of her vaccination or from prior infection) or she has become infected already. Either way, at this point neither condoms nor anything else will make any difference.
5) I know of no data that flat warts are any more likely than other warts to be caused by high risk HPV. Anyway, as a sexually active person, it's a good bet you've already had one or more high risk HPV infection. The high risk types are just as common than the types that cause warts, maybe more so.
Take a look at the thread linked below, which gives further information about HPV that you should find reassuring. You can find many others as well through this forum's search function.
http://www.medhelp.org/posts/show/1522088
So don't panic. Follow your dermatologist's advice, and encourage your partner to finish her Gardasil. Best wishes-- HHH, MD