Most people wait at least 6 months. Some wait a year. Very few wait 2 years. There is no right time for everyone. It all depends on how your body fights the virus. If more warts appear, then your body is losing the fight. The clock starts from the time that your last wart is removed while no others appea. Yes, you are less contagious when visible warts are gone however you can still infect someone. Some people take a lot of vitamins, supplements, etc or they lead a very healthy life, exercise, get a lot of rest and don't smoke cigs or drink alcohol. Some people think a strong immune system will aid in recovery but this isn't proven. For sure, cigarettes has been known to cause more warts. If you smoke, stop now.
Oral sex is never safe. Never was. However only people with oral HPV can pass it via oral sex, as far as I know. There is no approved medical test for oral HPV. If you have any doubts, ask your dentist for an oral exam. The good news is that oral HPV is not as rampant in numbers like genital HPV. But it seems to hit more people who drink alcohol and smoke cigs.