Where do I save the vault.dem file? I know that the vault.sav in SAVE folder, but where vault.dem?

Doesn't matter where you put it. The vault.dem file is just for you to include in your demo folder you want to submit. you just copy it into the demo folder of your pb, before uploading it.

Ok, thanks :)

speedrun_save vault will load the save "vault" instead of the first map. Then, LiveSplit will detect that it's speedrun_save is equal to vault and set up automatically