Directly to your questions. They are based on the assumption that the diagnosis of genital warts is correct.
1) There probably is little point in stopping sex with your partner now. She has already been exposed. The general advice to couples in which one person has HPV and the other apparently does not (and who have been having sex) is to not worry about it, just keep and eye out for warts and for women to stick with the program of annual pap smears.
Having said that, it is likely that infectiousness declines once the warts are gone, but there are no good data. It's a good idea to avoid direct genital contact with your warts until they respond to treatment, probably just a couple more weeks. You might remain somewhat infectious after that, but probably after 6 months there is little chance of transmission. Condoms reduce the risk somewhat, but in the long run don't make much difference--perhaps especially when warts are in a location that is not consistently covered by condoms.
There is never a problem with "passing warts back and forth". Once the infection clears up, you and she both will be immune to future infections with your virus.
2) Symptomatic oral HPV is rare. Probably lots of infections are transmitted to partners' mouths, but they don't get warts. I wouldn't worry about oral sex.
3) There are several other options for genital wart treatment in addition to "acid" (probably trichloroacetic or bichloroacetic acid), both provider-applied (podophyllin, freezing, laser cautery, others) and patient-applied including podophyllotoxin and imiquimod (trade names Condylox and Aldara, respectively). They all are equally effective, but some providers are most experienced with one or the other. If you want to consider other options, you should discuss it directly with your provider. Perhaps s/he will give you a prescription for Condylox or Aldara. However, those require treatment for 3-4 weeks, whereas just 1-2 more acid treatments might be all you need.
Bottom line: Probably it's a good idea to avoid direct sexual contact of the warts themselves with your partner's genital area until the visible lesions are gone, i.e. no vaginal penetration but no other restrictions. Once visible warts are gone, just go back to where you were, with your partner keeping a lookout for warts. You and she need to look at warts as a somewhat unpleasant inconvenience, but not a significant health problem.
This also is a good time for your partner to ask her own health care provider about getting the HPV vaccine. It's too late to prevent her getting your infection, but it will prevent future infection with other HPV types, including the two strains that cause most cervical cancer.
Good luck-- HHH, MD