Lorwyn-Shadowmoor is explicitly not part of the Forgotten Realms it's part of the Feywild which makes sense for it. And like wise the Moonshae make sense being connected to the Feywild.
I probably would have preferred something a bit more realm focused, but I am fine with this entry.
Domains of Delight are separate from the mirror part. They are sections anyone can get to from anywhere, as they are equivalent to Domains of Dread.They local Feywild is part of the Forgotten Realms. The Feywild literally is a mirror plane, so the part that mirrors Toril (and other FR planets) IS part of the Forgotten Realms, the same way the part of the Feywild mirroring Greyhawk is part of the Greyhawk Setting.
This is true of other material plane settings and it's also true for the parts of the Shadowfell that mirror these worlds, except Domains of Dread, which were carved off into their own setting decades ago.
Domains of Delight are separate from the mirror part. They are sections anyone can get to from anywhere, as they are equivalent to Domains of Dread.
You get that in Ravenloft too. The Carnival and the House of Lament for a start.You even have Domains permanently within Domains in the Feywild
They can if the archfey who rules the domain wishes.I don't even remember if they have mists
An archfey … can surround their domain’s border with walls of shimmering mist or some other magical effect that hides the domain from view and, if the archfey wishes, prevents creatures from entering or leaving the domain…