Yes, you can fold it with the pushchair seat attached, although it needs to be facing away from you to do it. Car seat will only go on rear facing, and I've never tried to collapse it with the car seat on, it wouldn't be worth it as it would the be very big!
It's handy for travelling through airports that it can be collapsed as one piece, some airlines are funny about two part pushchairs counting as one item.
Nope, I can't fold it with one hand, although this very morning my partner opened it with one hand!
No, I didn't get the carrycot, we had a moses basket on loan for in the house. Thought the carrycot was very expensive for the amount of time it would be useful. The seat goes down practically flat and is suitable from birth (not for a whole night's sleep though).
I also liked that the footmuff/apron/liner thing is lovely and cotton, a few of the other pushchairs I looked at felt very nylony.
Any more questions, ask away!