1) You don't need any sort of box for low voltage cabling. You can buy an
old work plastic ring if you want. I just cut holes in the drywall with a dremel (using a template) that were large enough to clear a 6 keystone wall plate, but small enough so there was still a decent amount of drywall where the screws needed to go. Then I put small plastic anchors in the drywall to hold the screws that hold the wall plates on.
2) I've always used the tool-less. When I first bought CAT6 keystones from Monoprice almost 3 years ago they were the only choice (there were no CAT6 punch-down keystones at the time). Since they're cheaper and they worked fine for me the first time I've continued to buy the tool-less one.
3) No
4) No. The patch panel comes with a plastic punch down tool that while cheap works fine for the job.