yamihonenukitenshi

First, the mage ID. You find it... *checks game again* Shortly after fighting Isaac fotr the first time. (here's a hint, when you're fighting him, steal from him, because you need it later. Like really. I have to restart cus I didn't think I'd need it, so I didn't get it)

And that door. You'll be able to open it after your Battle-type ID learns Brute Force. It's a skill that it learns. And finally the chair. That's a teleportation room. But, it's not active until you find another one. I've found like five so far and I use them a lot to get around so I don't have to backtrack all of the time. Does that help you?