Do Genital Warts Spread During Intercourse?

My boyfriend was just diagnosed with genital warts. I don't have any outright symptoms and I was checked (during a normal physical with pap smear) in between the time I was last sexually active and with him.

1. Could I have given this to him?
2. If not, could I have genital warts now?
3. Since he has it, does the virus stay with him forever?
4. He's gotten the warts frozen and was given a gel or ointment to put on it. It's supposed to clear up in about 8 weeks. Can we be sexually active prior to that?