1) I bought the usual cardboard replacement from Jim Carter. Have no experience with ABS, although I had a leak around the center of the windshield and the headliner got damp and came loose from under the windshield trim. But I was able to get it back in place and looking OK. ABS wouldn't be affected by moisture.
2) Definitely secure the front section to the middle bow first. Have a helper to hold the opposite in place as you tuck the headliner behind the windlace above the door. Your ball-end weatherstrip tool works well there. The windshield trim goes on after the headliner is in place, and the rear section and bow with it's screws would be the last thing installed. My wife was the helper and it went fairly well.
3) I used a rubberized sticky stuff for insulation/sound deadening and it seems OK. I would think that unless the foam is very compressible, it would be hard to install the headliner, as the space between headliner and roof is variable. IMO, that would be too much trouble for whatever improvement you might get.