The castle is right there, you'd think she would have noticed signs of life long before the kids showed up.
She doesn't know about the life of the former Saint, but the country that was involved with her, is Gone. Courtesy of Aiden. Also, Aiden can easily go with her? He has a Human Form, and the knowledge and experience to conceal his magic aura.I wonder where this story plans to go because Satsuki is kind of a foolish person so I would bet she is totally unaware of the actual danger her current and former identity actually put her in this world. She's also the kind of person that would say Aiden can't join her and unless Noir grows enough to learn polymorph she probably wouldn't let them join her either. She has no meaningful way to protect herself otherwise and her clothes would immediately put a target on her.
Frankly the safest place for her to visit right now is the Beastman village that's coming to pick up the kids. Everywhere else she doesn't even have the minimum necessary skills or knowledge to safely engage with.
Neither is really her world anymore, she only feels Home-like at her mountain, so like other isekai protagonists that can go back to Japan, it's the "Real" world and the Fantasy one.If you want all 3 asap, I think you want storage first. Can buy more in her world, store it for a long stay in the other world, and do more stuff to make points there without having to go back to her world. If you want go out now though, it's gotta be map. Getting lost in the wild without the storage upgrade is a surefire way to certain doom.
Also, does page 12 really translate to "the real world" or no? I'd expect it to say "my world" or something.