Yes. The reason for the 6 weeks 3 days is that we automatically add 2 weeks to the actually age of the pregnancy. We count from the first day of the last period. Because of this, when doctors talk about gestational age, a woman who is 6 weeks 3 days "gestational age" is actually only 4 weeks 3 days pregnant. It's confusing. A woman is automatically 2 weeks pregnant at the time the pregnancy was conceived. The reason for this confusing way doctors talk is that before the time of ultrasounds, the only way a doctor could figure out an estimate of how far along a woman is from the day of her last period. I hope that is clear. So to repeat, a woman who has sex one day and gets pregnant that day is "2 weeks gestational age" according to doctor talk. So your ultrasound showing 6 weeks 3 days gestational means you conceived 4 weeks and 3 days earlier. The error rate in ultrasound at this stage of pregnancy is about 3 days in either direction. SO the conception was anywhere from 4 weeks to 4 weeks and 6 days before the day of the ultrasound. Yes that is correct. Even a pregnancy from September 10th isn't possible with the information you've provided. It simply is not possible. Ultrasound technology is very reliable at this early stage of pregnancy. It would not be possible for the technician to make an error that large unless they were incompetent. It may be reassuring to get one more ultrasound to confirm again if you find yourself still worrying about it.
No. The early ultrasound confirms the due date and fixes the conception date. If you go overdue, it will be because some pregnancies go overdue. This doesn't change when the pregnancy was conceived. All babies grow the same rate for the first 12 weeks of pregnancy (with extreme exceptions, starvation, heavy drug use, etc.). This is why ultrasounds are so accurate at this time. Once past the first trimester (12 weeks gestational age), influences such as genetics, nutrition, etc begin to influence the rate of growth. Measurements of the baby at between 6 and 10 weeks are the most accurate way of figuring out the conception date unless there is only one possible known conception date. For example with fertility treatments or if a woman only had sex on one day. Anything else I can clarify? I hope you feel more convinced at this point. If you are still worried, get another ultrasound done to confirm the first one.
Yes that is a normal level. Estrogen level can be low despite a normal FSH in situations where the ovary just doesn't respond well to the signal or if a woman is thin.