Straight to your questions:
1) Assuming you have been sexually active before your warts were diagnosed, there is no point in changing your
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Sexual problems overview practices at this point. Your partner already has been exposed and probably infected. (The normal pap smear and exam do not prove she isn't infected. Paps and physical exams do not pick up most HPV infections, especially the types that cause warts.) She should continue to be checked for warts, but I see no reason to start using condoms or avoiding sex at this point. However, if your relationship is brand new--if she has not yet been exposed to your warts--then you should avoid sex (except mutual masturbation) until a few months after your warts have been treated and completely clear up. Also, she should immediately start taking the vaccine against HPV (Gardasil). She should discuss this with her doctor.
2) Condoms are good but not great against HPV. There is a lot of skin contact above the condom's coverage area.
3) There are no definite data on how quickly people with warts stop being infectious. Getting rid of the visible warts doesn't necessarily mean the virus is gone. Most experts believe that it's best to wait a few months (e.g. 6 months) after the warts are gone, and there is no recurrence, before resuming sex with susceptible partners. But as I said above, you can safely assume your girlfriend already is infected so it probably doesn't matter much.
4) As I said above, her doc cannot know she doesn't have HPV. Assuming you had unprotected more than a few times before your warts were diagnosed and treated, she has been infected. Her immune system might have already cleared up and asymptomatic infection; or she might go on to develop warts in the next few weeks. Also, depending on when your relationship began and when you last had sex with other partners, she might herself have been the source of your HPV infection.
Good luck-- HHH, MD