So every week you have your progress saved to Coil depending on how far you've gotten.

If you go in and beat turn 2, you can't go back with anyone else to beat turn 1 until the Monday reset. (When your save is wiped so you can run the dungeon again.)

Most people run it with a static party, rather than just helping random folks, but there are also lots of linkshells dedicated to running it, so I'd recommend getting yourself set up with one of those.