hi ess - Sorry that you had a horrible time of it.
I hope I can help with some of your questions -
Should I have been given the scan when I was first admitted? - If you were bleeding, its obvious that you have had an abruption, but even a lot of blood can be caused by a very small bit of placenta lifting, and a scan only picks up less than 50% of causes of bleeding anyway, so not much point really.
Should I not have been induced then, considering I was a week overdue and bleeding? - Most places probably would have induced you in case of further bleeding, seems a bit odd that they sent you home, but each hosp / doctor would have their own ideas about this.
Was the scan at 36 weeks accurate? - You will never know the answer to this, but placentas generally do move up as the uterus grows. More likely that he questioned the high part as opposed to the fact that the placenta was out of the way of the os. Its a little unlikely that it was high, as is usually used to describe a fundal (top of the uterus) placenta, but was high enough to be considered safe for vag delivery.
Was it negligent of them not to have scanned me before I was induced - as before, there was no real benefit in scanning you, so not negligent
Surely a placental abruption would have showed up and I would have been given a c-section? - a placental abruption can be a reason for a c/s, if it is big enough or baby is distressed, but the majority of women who have had bleeding in pregnancy (aside from cervical) have had an abruption and most dont need a c/s. It is a reason to get baby delivered and so you were induced.
It is really common for labour to progress quickly with bleeding as blood is an irritant to the cervix and often seems to make it dilate quickly.
It sounds like you had a further detachment of a bit of the placenta at 9 cm, which baby didnt tolerate well and they did the right thing by taking you for a crash c/s. Standard policy is to do a quick VE before the c/s starts, just in case you are fully dilated and they can deliver baby by forceps, or if the heart rate is ok, by pushing, if its likely to be quick, which sounds like what happened to you.
Baby would not be cold at delivery as she is at your body temp, but she may have got cold while being with the paed.
The retained placenta was bad luck, and with abruption and retained placenta, its not surprising you lost a bit of blood.
Although it is very traumatising for you and your partner, everything seems to have been done correctly and certainly does not sound negligent or dangerous, however, because it is probably happening quite quickly, with lots of people running around etc, it can be very traumatising for you both, and your partner probably thought he was going to lose you and baby when you went into theatre.
I think its really important to debrief with the hospital if you can, and it would be very worthwhile to get in touch with the birth trauma association for counselling.
I hope this helps.