(1) No idea. I think in the past they've used a metal mesh (which neatly lets resin rise through it, and also gives something for the plastic to grab onto). Presumably other things will work too.

(2) You probably shouldn't be changing the entire setup for every print. Pick a container, get the Peachy set up above it, calibrate it for that specific setup, and re-use it for all subsequent prints. I think they were planning to do a series of calibration patterns that can be used to get the positioning just right (eg. print a 5x5cm square, if it's not square then adjust the Peachy until it is square) and tuning the vertical axis is just a matter of measuring the container.

(3) You'll lose resolution at very large sizes, due to the limited angular resolution of the Peachy and the laser going out of focus. Very large prints would also take an extremely long time, because (as you've said) the dripper will take days to raise the level of a bathtub-sized container, and also because there's a limit to how quickly the laser can cure each layer of resin. And, of course, a bathtub full of resin will set you back a few thousand dollars. Realistically, the answer is likely to be that the maximum possible print size is much larger than the maximum practical (in terms of time/money) print size.

(4) For the basic Peachy, it appears that the Peachy itself is provided and the user provides everything else (print container, water reservoir, print base, Peachy support stand, etc).

(5) I think it just uses the standard UV-cured resin, so "multi-purpose" UV-cured resins (like those sold by MakerJuice) should work.