Thank you for the question and I am happy to help.
First, with regard to the 'vanishing twin' phenomenon - this is actually common in the fertility clinics. Perhaps it occurs frequently with non-fertility patients too and one explanation is that:
1. They are increasing the risk of twins with whatever treatment they are pursuing
2. They are performing earlier ultrasounds than are performed in the regular setting
I have tried to find evidence for you of problems related to loss of one twin early in the first trimester and can find no evidence that this is associated with adverse outcomes beyond the risk of miscarriage of the second twin (which currently is not a concern in your case). Loss of a twin in the second or third trimester is a much bigger deal but, again, this does not apply to you. It is perhaps a finding that is related to the fertility clinics and the patients whom they are treating: they are older and perhaps more unhealthy in some cases.
Miscarriages are common and for reasons that we do not know, most of the time. Most twins are not identical, so whatever was wrong with the one twin is very unlikely to be an issue with your 'surviving twin'.
Finally, if you had first trimester sceening that placed the risk of DS that low, then the need for the quad screen seems silly. I do have patients have an AFP drawn at 16 weeks, but this is a screen for spina bifida (unrelated to DS). Yes, it has a sensitivity of picking up a kid with DS of >90%, but it is really just an adjusted odds ratio - your 'odds' are not zero, but they are very low. If you NEED to know for sure if you have a child wit DS, then you can have a test called NIPT drawn (you can google this for more information) but it might be that insurance does not cover it.
Does this answer your question?