Yes, gonorrhea (as well as chlamydia and syphilis) can be transmitted via oral sex. In fact, I know of someone who contracted oral gonorrhea (at first she thought it was a bad sore throat) and passed it to a guy who contracted genital gonorrhea.

Yes, oral-genital transmission (and vice versa) is common. It can even infect the mucous membranes of the eye in some cases.

Can it be transmitted from heavy kissing?