Welcome to the forum. Thanks for your question.
Your girlfriend is overreacting. She's not alone; these days there's a lot of confusion, and inappropriately inflated fears, about genital HPV. The fact is that everybody gets genital HPV, often several times; it's a normal, expected, and largely unavoidable aspect of human sexuality. Fortunately, the large majority of infections cause no symptoms, clear up over time, and are not serious. I encourage you and her to look at the following threads for a more detailed discussion of these and other truths about genital HPV.
http://www.medhelp.org/posts/STDs/HPV-Transmission/show/1522088
http://www.medhelp.org/posts/STDs/HPV-without-sex/show/1799277
To your specific questions:
1) Yes, this is correct. Her HPV infection probably cleared up long ago and it is unlikely she could transmit it to you at this time, 6 years after her diagnosis.
2) Gardasil would protect you if she is currently carrying one of the HPV types covered by the vaccine. However, it isn't a guarantee; Gardasil protects against the 4 most important HPV types, but not against the 100+ other strains that exist. Also, the vaccine isn't fully protective until after the third dose, at 6 months (although there may be subsantial protection after the second dose at 2 months).
3) The vaccine is effective at any age; it's not recommended beyond age 26 primarily because it hasn't been much studied in such persons, and because new HPV infections are not common after that age. Because of the official recommendations, health insurance may not cover it -- but if cost isn't an issue, there is no reason you could not be vaccinated.
Your partner has a skewed perception of HPV. There are many sources for more information; she could start with information provided by CDC (www.cdc.gov/std) and the American Social Health Association (www.ashastd.org).
Best wishes in your relationship, and in helping your partner understand the truths about HPV. It really shouldn't be such a big deal for her!
Regards-- HHH, MD