The nickname "topsiders" are because people like Asuna and Morisaki literally live on the top side of Agartha.
It can also interpreted as a clever insult saying that the "topsiders" think they're "always on top", meaning that they believe they're superior to any other beings.
Why does Morisaki choose to stay in Agartha? Well aside from the whole "new fresh start" idea, Morisaki was also a part of Arch Angel. So, they're probably still after him for his betrayal.
Plus, he's extensively studied the language and culture of Agartha, making the adjustment all the easier.
Remember how Mimi was able to talk to the deer-like Gate Keeper. It turns out he's from Agartha. So, Mimi is probably able to communicate with them.
With Asuna, this movie deconstructed pretty much every single adolescent Star-Crossed Lovers from Shinkai's previous works, from Voices of a Distant Star to 5 Centimeters per Second. All those main characters spend most screentime thinking of the feelings about their love interest instead of actual person-to-person interaction, yet somehow the longing is still strong despite the separation of time and space. At first, you would think Asuna would fall into that category but later she realized the real reason why she came to Agartha: It is not because of her love for Shun but the loneliness that had haunted her ever since her father died.
Asuna is implied to be half-Agarthan on her father's side, explaining how she got the clavis, and why the Izoku target her for her 'defiled' blood — they don't target Morisaki, despite also being a topsider, but they do target Manna, who is half-Agarthan as well.
Morisaki commented early in the story that he didn't know how long he and Asuna would be gone. That being said, how long has Asuna's mother been without her only child?
It's already been established that many of the people of Agartha hate "topsiders". And it was revealed by the Amarout village elder that Mana is of mixed race between topsider and Agarthian. With that knowledge and the scene we saw with that brat throwing a stone to Asuna's face...could Mana be a constant target of bullying and harassment?
Asuna manages to return home and that's great, but do the Arch Angels still remember who she is?
The whole matter involving Morisaki willing to let Lisa inhabit Asuna's body. Even if the body was seemingly transformed, that's still a middle-schooler in origin, creating a whole level of Squick if things had gone unopposed. Worse yet if her body didn't actually change and the 'water' over Asuna merely gave her the appearance of Lisa.
