Courtney,
If your cycle is fairly regular it seems plausible that a doctor could pinpoint conception to within a ten day time frame by calculating from the first day of your last period. The size and development of the baby on the sonogram can also be used to determine and clarify the stage of the pregnancy and the time of conception. If the doctor says you conceived at a time that the child’s father would have been your boyfriend, who is now accepting responsibility and plans to stay with you in raising your child, then I probably would not worry too much. Does Ken know that you have questions about the baby’s father? If you are sure that Ken is the father, then it might be best to just leave the matter alone and not bring it up. However if there is doubt about who the father is a paternity test could be done after the baby is born. If there is a serious chance that your boyfriend might not be the father, he deserves to know.
Pre-ejaculate contains sperm cells. I don’t have statistical figures. I would guess that the chances of pregnancy are less than with ejaculation, based on volume of semen. However pregnancy from sperm in pre-ejaculate can and does happen.
Kate