"What are men to do when there is no test?" For the most part, men and their partners should just sit tight and not worry about it very much. Please see my reply to another question earlier today:
http://www.medhelp.org/posts/show/365097.
HPV 16 and 18 are among the most common of all HPV types, but they do not cause warts. It is true that the types of HPV that cause warts, mostly HPV types 6 and 11, do not cause cervical cancer. (Why you doubt the CDC information, by the way??) However, HPV 6/11 infection often causes low-grade pap smear abnormalities which, if left alone, do not progress to cancer.
So, if your penile bumps were warts, they may or may not be related to your partner's abnormal pap smear. That said, my bet is that your problem and hers are unrelated: the timing suggests your warts had cleared up and that most likely you were no longer carrying the virus when you and your new partner first had sex; her problem could just as easily go back to some previous partner.
However, you're never going to know for certain, and it doesn't matter. The appropriate attitude (and the mature attitude) toward HPV is that everybody gets one or more HPV infections somewhere along the line; they are essentially unavoidable; that most infections never cause serious health risks (even the high risk types don't progress to bad disease with appropriate medical care); and that it is foolish for infected couples to try to figure out who was infected first. The blame game is always a loser for both participants.
I think those comments answer questions 1 and 2. As for question 3, there is nothing to be done. Since you and your partner had already had sex, there was no reason to stop once she found the bumps. (It sounds like she needs some education that not all bumps are warts, whether or not they started out that way. But if in doubt, the two of you could go together to a provider who could educate her after examining you.) Anyway, avoiding sex with partners with known HPV doesn't reduce a person's long term risk of catching HPV somewhere along the line. Anybody who ever changes from one sex partner to another from time to time is sure to have sex with one or more people with undiagnosed HPV--and that most commonly involves the high risk types.
You already are aware of the vaccine. Your partner should have it. See my follow-up comment in the same thread I cited above. Also, please see the other websites I suggested in that thread, and read up further on HPV.
Good luck-- HHH, MD