If a Tachikoma can develop a ghost, a system like the basis of SAO/Alfhiem can too. I'll believe Kayaba was smart enough to develop a psychological analysis subroutine that developed a consciousness as it progressed, since it's purpose was to mimic and understand human psyche.
As for her fairy arc, RECT copied the SAO data directly from an older build, and reskinned it. Both because they were too lazy to code their own game, and the douchebag wanted to capture test subject and Asuna (being the company head's coincidentally trapped daughter). We find out later SAO fans ported the skill system into Alfhiem (and all of SAO anyway), so we know they're compatible.
Yui was afforded all the same access levels her program used to have, and the game just changed her accordingly, the same way Kirito's stats were corrupted during the import (same Username in the database) and interpreted. All the console command IDs were identical on his stats and gold because the game was the same engine. Only the items were a problem.
That part made perfect logical sense to me, and it was properly set up to do so. The only miracle was her item wasn't corrupted. Eventually, Kirito probably would have modded her in.
As for her being stored locally in Kirito's nervgear, that's a conceit I'll just have to let them have. Just assume their hard drives and processors are a lot better than our own.