LogFAQs > #902136051

mystery rooms have npcs that you can talk to get items or get bonuses on your item from
talking to npcs enough will almost always trigger a battle, and wiping everyone out in that battle will give you "training bonus" for your item
the 3x3 formation of the cat monsters is supposed to be an exp gaining area whose fight you begin by talking to the cat in front a couple times

if you get caught in one of these mystery room battles and need to escape, you can use someone to displace the item world guide catsaber npc to access the exit gate underneath it (it's still there in the bank room, but it isn't visible)