Check the due date they gave you, (and in fact check all the details and dates you listed above, the earlier ultrasound, your period, when the ultrasound was and all) because July 12 doesn't go with the same people saying "8 weeks pregnant" on December 7. But July 12 does rule out the sex in September.
- When you were on an IUD with a hormonal aspect, it's not like pulling a cork, as in after pulling it you have zero protection. The hormones will have lasted a little while. You would not have ovulated immediately upon its removal. (But that doesn't matter anyway because ...)
- The five-day bleed in October sounds like it can only have been a period. Taking out a coil doesn't make you bleed a month later. If anything, it might have made your uterine lining a little thicker (because of the hormones), which would explain why your next period was a bit heavier, since it was clearing out the lining. (But that doesn't matter because ...)
- A medical person saying 8 weeks "pregnant" means your medical time frame for the pregnancy began 8 weeks ago, not that conception was 8 weeks ago. Medical people begin the count of pregnancy on day 1 of your previous period, or a calculated day 1 if the ultrasound indicates it. 8 weeks pregnant does not mean conception was 8 weeks prior to the ultrasound, it means your conception was 6 weeks prior to the ultrasound.
- You're lots better off doing your calculating and worrying using the estimated due date (EDD) from your ultrasound, not getting wrapped around the wheel of what "8 weeks pregnant" means. Did they give you an estimated due date of around August 2? Whatever date they did give you, you can put it into a conception calculator online, and it will tell you an estimated conception date. Or, just count manually on a calendar backward from the due date, 266 days. That will give you an estimated conception date too.