Slurs across movements and "attaca" related problems

How would you do the slurs across flows like in this page :

Also how do I do the cautionary key signatures? (The movement 4 that comes at the very next page as a different set of instrument)

Simply use a system break instead of a new flow. This flow is Nº 2 and 3 (or more).

The OP is asking about the slur that crosses the flows. I’m afraid you will need to use the l.v. tie workaround. It’s been described at length many times in the forum.
L.v. Tie Workaround