Very unusual situation. Thoughts?!

Samantha
So ladies. Here is the story, I'm sorry it's long! 
I had a MC back in May after falling pregnancy very quickly from when my husband and I decided to TTC. I was an outpatient at the hospital for some weeks as my HCG wasn't dropping as it should, which was distressing and made the whole situation long and drawn out. 
My HCG finally went back to normal and I had a period on 1st June. My husband and I decided to not try this cycle however, as we were going on holiday and wanted a bit of a mental break after our loss. We BD just after my period finished then abstained for almost 3 weeks to ensure I didn't get pregnant before my next period. I also tracked my ovulation with OPK's. I ovulated 8 days after we had sex for the last time. 
When we left for holiday my period was late, but I put this down to an irregular cycle due to MC as I was sure I couldn't have been pregnant. We then went on holiday and went back to baby dancing. 
5 days later, my boobs were sore and I needed to pee A LOT! I took a test and there was a very very faint line, which confused me as I must have been about 25 DPO. I put this down to a dodgy pregnancy test which cost me 50p, stopped drinking and re-tested when we got home. This time it was a BFP! I must have been 8 weeks pregnant from my last period. 
Because of the previous MC, my doctor suggested I go for an 8 week scan. I couldn't have this on the NHS so went private. The sonograpger told me my dates did not match up, as there was a gestational sac, but no yolk sac, so there was potentially a problem and the baby may not be developing property. I went back to the EPU today, and the sonographer there said she could see a yolk sac, but I was only 4 weeks pregnant. Sooo ladies: 
- Is it possible that I got a faint positive just 5 days after BD?
- Is it possible I had sore boobs and needed to pee a lot just 3 days after BD? 
- Is it possible that I ovulated twice within one cycle without having a period in between? 
So many strange factors here, I have my fingers crossed for a little miracle, but from the above, sounds unlikely 😞.