ice magic works great
There is a cave south of Figaro mixed in with the mountains
in kevins house
You get it after you beat Hecatoncheir in the Cave of Shadows.
Cave in the underworld at in the western part of the map
You have to get through the Sochen Cave Palce to get to Old Archades and then it will explain itself
The Skeleton Key is actually not an item as you would expect but a button of sorts. In the Sealed Cave of Final Fantasy III there's a dead end with skulls. One of these skulls is the actual key you need to interact with to proceed.
The Dwarf Cave can be reached by sailing to the north west corner of the Aldi Sea. Land at the port there and then walk south to find the cave entrance.
Edward gives it to you when you visit him in Troia castle, before you go to the Magnetic Cave.
Once you sail through the canal, head north to the town of Melmond. There you will hear stories of a vampire attacking the town. Head south to the Earth Cave and defeat the vampire. If you go a little further you will find a stone slab that you cannot move. Head out of the Earth Cave, and head north west to find the cave where the sage Sarda lives. He will give you the Rod which will help you move the stone slab. Descend to the bottom of the Earth Cave and defeat the Fiend of Earth.
There are no caves and therefore nowhere for the cave monster to go. So, if there was such this it would be a outside of a cave monster.
you find him in the snow realm when you defeat the crab monster in the cave to lead to the sand sanctuary.
Yes, you need the Hydra scale as one of the five sacred items to fulfill the quest.