Questions about gay sex?

There are three issues here that you need to be wise about. The first is why did he contract the infection in the first place. Yes we know how, but why? Were you in a relationship then or is that more recent. And if you were not, why was he not practising safe sex (condoms). That leads on to are you sure he can be trusted to be faithful only to you. Unprotected sex is risky unless both parties have total commitment to each other and are honest and open about their sexual health. If he has a history of being a bit promiscuous, then has he changed that much or will he get tired of the same guy topping him. Questions you both need to explore before you risk your own sexual health for the sake of a condom or six. Then seeing as he has been treated for the infection, why has he not shared with you the advice from the doctor, who would have clearly giving him specific information about the period of no sex. Another question that makes me wonder if he actually cares about you or himself. He can ring the clinic that treated him and ask the question, when can he resume sexual activities. Or you can ring them and ask the general question. Monogamous means much more than what perhaps your boyfriend realises and you would be wise to debate it further before you put all your trust into one pot, so to speak.

you're very cozy, about gonorrhea I learned that this virus is permanent in your body and from time to time it shows on the penis. Then after 4 to 5 days it disappears, but it will come back even after 1 year or so.

Gonorrhoea is a bacterial disease, not caused by a virus. And it is curable by antibiotics (provided it is not resistant to the specific antibiotic used). You should take the advice of the particular doctor who treated him. However if he had one STD, he may have acquired others. Do either of you have sex outside the relationship?

I don't know, has his doctor told him he's free of the virus? Getting treatment isn't the same as being cured.

After about 6 months with no systems, you are most likely safe.

I would be consulting a doctor instead of acting out first.