What is it, young man? Embarrassed to be seen walking around with an old crone like me?
Unei is a mage who lays in a deep sleep in her shrine, her parrot familiar keeping an eye out. It is only after the Warriors of Light seek out Noah's lute and play it per Doga's instruction that she awakens. Upon waking up, Unei leads the party to the Battleship Invincible, before leaving them to track down the remaining Fang necessary to reach the Syrcus Tower.
Unei is the second of the three mage students of Noah and zags where Doga zigs. While suggested to be a master of magic, Doga sticks primarily to Black Magic spells in contrast with Unei who uses White Magic. Doga is dead serious while Unei is more playful, taking a moment upon waking to catch up on her exercise. And while Doga's cloak does not make his age entirely clear, Unei is clearly an old lady, something she doesn't pretend to deny.
Unei inherited mastery over the Dreamscape from Noah, but this doesn't come into play much. It's mostly her using a piece of rock from the dream world to destroy something in the real world.
Like Doga, she attacks the party and forces them to kill her in order to create the key to Eureka. Unei supports the kids with Doga, eventually sharing her soul to revive them and give them a shot at stopping the Cloud of Darkness.
The remake builds upon Unei in a couple of ways. For starters, her connection to the Dream World is emphasised a bit more, as she now appears to the Warriors of Light while they're unconscious from the Cave of Tides' collapse. It differentiates Unei from Doga via her interactions with the Warriors of Light; While Unei was always casual, it comes across a bit better here. That's not to say that Unei can't be business-focused either; A new interaction has her mention that she was unaffected by the time stop due to having been in the dream world. There, she noticed some force that attacked the floating continent and that Xande himself was also affected by the time stop, meaning he couldn't have done it. Unei also shows clear concern for her fellow student, expressing disbelief at Xande's actions and lamenting that he couldn't see his gift for what it was. Heck, she even asks the Warriors of Light to save Xande, presumably from his own madness.
In battle, Unei primarily uses White Magic spells, notably Holy.
The unused content, once again, adds more elaboration. Unei mentions that she's known Xande since they were little (which adds implications regarding the nature of the apprentices under Noah), mentions that mages such as she and Doga can come back to life easily magic (explaining how Doga is able to round everyone up as well as the nature of their immortality) so Noah left the most powerful of the three, Xande, mortality as a reminder of how precious life is and laments that she dreamed of Xande repenting and wishing that that were the reality and "Demon King Xande" was the dream. She also expresses guilt over Xande's fall to villainy, noting that she was in the Dream World and could do nothing.
While not related to Unei herself, the Temple of Time has a minor subplot where Luneth and Arc delude themselves into thinking that Unei is a sleeping princess, a common fairytale trope. Needless to say, they are thrown off by Unei's true appearance, although she mentions that she was quite the looker back then.