How exactly do server clients and such work? Like Jade was Dave's server player which got him into the game, Rose was John's. And then what Dave got Rose in and same with John to Jade. Was there a specific disk/way they or the game chose them in that order or was it just kinda random?

It’s just the order in which you go in. You have a choice in the order, however different meteors head towards the houses at different times, so ultimately there is a time constraint- Dave couldn’t have been the last one to Enter, for example, because he only barely managed to Enter before the Meteor Landed. In fact if it wasn’t for Bro snapping it in half, the Meteor would’ve hit Dave.

However in a place with no Time Constraint, say, with a Void Session, you could really enter at any point and in any order.