It's basically a sleeping bag without a zipper. Guess it saves some weight(?). Some have closed foot boxes (lower third), some have a 1/3 zipper so you could actually open the quilt all the way like a blanket.
Yup, you sleep right on your pad with the quilt over you like a blanket. The idea being the part of a sleeping bag that you sleep on provides essentially no insulation since it's being compressed, so why have it.
I don't like the feeling of bare skin on the pad so I always bring a thin pair of long johns or sleep in my hiking clothes.
You don't need a special pad. There are some matched sets- pad and quilt- I think from Big Agnes- but other quilts come with straps or cords that go under/ around the pad. I like the straps the best. The cord you wrap around the pad and the quilt has clips that connect the quilt to the cord. You can slide the slips in and out to create as much or as little cocoon effect as you want.
Take a look at the video here to give you an idea of how this particular quilt works.https://katabaticgear.com/products/flex-22-ultralight-quilt