If your pap has still come back abnormal then yes, you are contagious. Even if your pap comes back normal, you can still be contagious according to my Dr. Men are most often carriers, they don't show normally symptoms of HPV. But if he contracts it he could then give it to future partners.
Yes, unfortunately it is still possible for you to transmit HPV to your partner even with a condom, but it is less likely. For instance if your fluids came into contact with any part of his penis he could contract it. And while it might be possible for him to contract throat cancer from giving you oral sex, it is extremely rare.