Dragon's Den... It's gonna happen

Does this require event editing? Is that how the switches and such work to navigate the dungeon with 3 parties?

Well switches and such are event triggers with an event "linked" to them, same things for NPC. You can take a look at FF6LE to see event triggers on some map with the event offset. Now looking at that offset in the event dump will giving you the detail of the event, that you can also lookup in a hex editor to understand better.

How to make the dungeon ask for 3 parties instead of 2?

The party selection is done with event command 99:

Code:

99 : 4    : Invoke party selection screen (A groups). Forced party members in bitfield B/C.

So I guess 99 03 00 00 would allow 3 parties to be selected. If not then look up the Kefka tower event on the WOR map and you'll get your answer.

The party switching is made by activating an event bit:

Code:

CA/03B3: D2    Set event bit $1E80($1CE) [$1EB9, bit 6] (Enables party switching with the Y button)

How to disable the Cyan's dreams event, the Hidon event, and the zone seeker event.

For Cyan's dream, by removing the corresponding event trigger. As for Hidon I'm not sure how and when the cave appear but it's also a map event that can be removed/edited.

Note that you have some empty maps that can be used to make an extra dugeon, I'm not sure if there is enough of them to have the Dragon's Den.