Hi Piper!
The stroller should fold completely flat rear or forward facing. Removing the front bar will make it lay even more flat.
I'm not sure about the Graco car seat issue. I would think it should fit snug.
As for the bassinet seat, this stroller does not have a bassinet attachment. However, you definitely do not HAVE to have one for your infant. Both of my kids and most (if not all) of my friends kids safely and comfortably used the infant carrier/stroller combo.
Hope that helps! :)