HPV-  Congratulations on getting vaccinated for HPV- that's the single most important thing you can do to prevent HPV infection and the relatively rare occurrence of HPV-related cancers.  If your wart was entirely removed by your biopsy, that may have entirely cured your HPV infection.  If not entirely removed, your risk of cancer is negligible.  Most genital warts are caused by HPV strains not associated with cancer and whether or not a cancer-associated strain, over 95% of HOV infections resolve, with or without therapy over a period of 1-2 years.  I would assume that your active HPV infection is a thing of the past.  FYI when HPV infections go away over time, small amounts of HPV DNA can still be detected using sophisticated research tests which can be the source or occasional recurrent viral shedding but that is negligible and not a problem.

There are no tests for HPV in men but as I tried to indicate above, this is not something I'd worry about.

There are no meaningful interactions of HPV and HSV.   Was your HSV-2 infection diagnosed with a lesion swab?   FYI, HSV-2 is virtually never transmitted through sustained open-mouth kissing.  Transmission of HPV from your mouth should not be a concern (I'm presuming your wart was a genital lesion, correct?.  Even in the unlikely circumstance that it was oral, risk of transmission through open mouth kissing is negligible and not a concern

I hope this information is helpful.  If there are additional clarifications, please use your up to 2 follow-ups for clarification.  EWH