1. Sew right through that batting. Quilters have been doing it for eons.
2. I always use pins.
3. I'm not sure myself, but I would guess that what you could do is sew two sides made of outer cloth|batting|inner cloth (feel free to have the edges hanging out on that one), then put both pieces wrong sides together and bind them up with the bias tape you've got.
4. I'm pretty sure you'll be okay with a straight stitch.