- I'd say go for a rolling, maybe do updates on weekends
- The students will very likely appreciate the customizability of Plasma or Cinnamon; if you want them to focus on work, GNOME (probably with some extensions) would be better. Tilers are a bad idea, because they take some getting used to
- Doesn't really matter, company distros might be paid tho, and that can obviously get expensive
- Wayland if your DE has good support (i.e. is GNOME or Plasma), otherwise X
- Btrfs' snapshotting capabilities might be useful to rollback the system to something working if the students fuck something up
- Immutable without sudo access should be the safest to hand over to people that you don't want to ruin anything
- I don't know enough about specific purpose distros
If you already know Nix, NIxOS would be a good choice
FDO is FreeDesktop dot Org, the XDG people
Vaxry is an asshole (the Hyprland maintainer)