Take some time to read threads on this board before proceeding. It could save you a lot of trouble!
The only batting I know that could stand to be quilted 16" apart would be Warm n Natural (and even that would be stretching it). The quilting is what keeps the layers together and prevents shifting. WnN is needlepunched through a scrim, which makes it much more stable than other battings. If you tried to use a regular polyester or cotton batting with quilting 16" apart, you would have disaster on your hands after a washing or two.
Yes, the quilting goes through all three layers. There are many tips that are helpful for layering and quilting, so that you don't get unwanted puckers and tucks in the backing, etc.
Are you planning to hand quilt or machine quilt?