I am also unsure of what to do at second door in snow village (it's called "glacial grotto entrance") looks like another flame core is needed but idk
Yup, that's the ticket. You have to progress through the story to be able to get to the second fire core thing to use it on the wall, battle Glace again and acquire her as equipment. I forgot the order of the story, but some helpful users have posted their walkthrough for the next pieces of story in this version.
If you haven't encountered her, try going to the guild, where you need to talk to Bern and he'll give you a quest. The first time you actually meet Glace is a scripted battle, and that grotto is your chance at a refight on a later point.
Also, be warned, I recommend raising the puppet's level to its maximum (10) in case you lose to her or wear her for extended periods of time. You'll see why.
Also also, someone here mentioned something about an enemy exclusive when you acquire all cursed items. Where is that enemy? Heck, *what* is that enemy? Any chance to trigger it when activating all cursed abilities? I swear there was something like so, or maybe someone mentioned it but piqued my curiosity.
Or maybe I imagined it ._.