It is time for you to celebrate! Your body got rid of the virus on its own!
1) Your children might carry your antibodies for hep C for 18 months after birth. There is however no risk of them becoming infected with the virus, since the virus is GONE! The antibodies just show that at one time in your life you came in contact with the virus, and since additional tests have shown you do not have an active infection - you are homefree!
2) None
My limited understanding is that anti-bodies are always produced when we are infected, they are our bodies attempt to clear the infection. With Hep C, the antibodies are not effective. So, the antibodies are not Hep C, they are your bodies defence mechanisim, they are harmless, it is irrelevant if you pass them on to your children, and you will not get sick from them.
It appears you are one of the lucky ones, who naturally beat Hep C. You were infected, but it looks like your immune system killed off all the infected cells. If you just had a clear PCR test 2 years after antibody discovery, I think it is safe to say you have not got Hep C and cannot pass it on:-)