First, I don't know what you mean by 'I noticed signs of a new HPV infection'. Do you think you have warts? Has that been diagnosed by a health professional? If not, stop speculating and get checked out. Until then, the rest of your questions are speculative.
1) If indeed you have genital warts, it is more likely a new infection. Recurrences 5+ years later are uncommon, and the chance of recurrence declines with time. 2) Entirely different HPV strains typically cause cervical/Pap smear abnormalities and genital warts. 3) If you have genital warts or other HPV infection, your partner is already exposed and probably infected. At this point there is no reason to stop having sex, to use condoms, or otherwise change your sexual practices or habits.
Bottom line: Get a professional diagnosis, then (and only then) feel free to come back if you have HPV or warts and stil have questions your provider can't answer adequately.
Good luck-- HHH, MD