Greetings Elora,
I think, "arrow rain" and "arrow storm" is fine

Although "rain of arrows" sounds better, "spell book of rain of arrows" doesn't
Yes, most alcoves in the game don't respond to such actions. This one let's me put stuff in it, and then rejects it, telling me it's full, but it isn't.
On the other hand, as someone else also stated before, it would be nice to be able to look through the maps of other levels for reference.
So, after the update, the "not yet accessible" part of the map will be available?
Looking forward to the new levels!
Best regards,
Emrah