[daedalron]

Again, answers in spoiler.

Spoiler:

New Aincrad and ALfheim is the same thing. New Aincrad is a place inside ALfheim, like the sylph city Swilvane is. So Yui follow her parents where they go, be it on the land, or the castle in the sky. At the moment of Extra Edition, the appartment in which Kirito and Asuna both live in-game (the place where they first talk about the whale) is in the World-Tree city. They both wish to get back their old house from SAO when the corresponding floor gets available again, though.

After the events from Fairy Dance, and her almost erasure by Sugou, Yui is not stored on the ALO server, but on Kirito's computer. So she can connect from there to the ALO servers, or the phones of her parents, or the internet.

As for some interface for Yui to use to get access to the outside world, at the moment of this movie, she has used a limited interface, on Kirito or Asuna's phone, to see a bit of the real world, and stay in contact with her parents when they're offline. But it's still limited by what the camera on such a device can record.