Welcome to the forum. Thanks for your question.
Assuming the diagnosis is correct, it isn't possible to know when and where your partner was infected. (FYI, all warts are caused by HPV; there's no such thing as a non-HPV wart.) Warts typically appear 2-12 months after catching HPV, but it can be 2 years or more. Also, previously acquired HPV infections -- sometimes years earlier -- once in a while are the cause of apparently new warts. I'll go directly to your questions:
1) There are two HPV vaccines. Gardasil protects against 4 HPV types, including the 2 types that cause ~90% of genital warts (HPV 6 and 11), as well as the 2 that cause 60-70% of cervical cancer (HPV 16 and 18). Cervarix covers only HPV 16 and 18. Do you know which type you had? I'm guessing Gardasil, which became available in the US before Cervarix and might have been the only vaccine available 10 years ago.
Vaccine protection probably lasts 10 years or more -- so the odds are you are not susceptible to your partner's HPV infection. However, 10% of warts are caused by other types, in which case you could be susceptible. It's also possible you had HPV 6 or 11 before you were immunized, in which case it is conceivable you have had a recurrence -- even if you haven't had symptomatic warts.
2) This definitely does not mean either of you has had other partners recently. Of course it's an STD, so that's always a reasonable issue to consider. But if you have no other reason to trust your partner's fidelity, you should trust him on it.
3) As implied above, he could have been infected since before your relationship started; or you might have an undiagnosed (recurrent) HPV infection that was transmitted to your partner sometime in the past several months.
HPV is very sneaky, and it usually is not possible to ever know with certaintyt he source (when, where, or from whom) of a particular infection. And for the most part it doesn't really matter. You should be on the lookout for warts, and you should continue to follow standard guidelines for periodic pap smears. But otherwise don't let this incident bother you. It's genuinely an inconvenience, not a serious health risk.
FYI, here is the link to a thread with a detailed discussion of HPV issue; and as you will see, it contains in turn links to a couple of other threads. Together these should give you a pretty good idea of the complexities and uncertainties about sexually transmitted HPV.
http://www.medhelp.org/posts/show/1269909
I hope these comments have been helpful. Best wishes-- HHH, MD