Her name would be rewritten as: Ashari'Nylireh ra'Kurah Sundancer (so same but just written differently). (Also, ignore Ishanna/Kalari's name style. She was special and as such her name was different

)
Yes, they prefer to bond gods or celestial beings (arch angels or angels or whatever else there might be) but will also bond immortals who have a less likely chance of dying, at least like mortals can die so easily. They have an innate desire to protect humanity but tend to view themselves as better because...well, they are by technicality. Some are humble enough to not be so vain so that will depend on the personality you want her to have.
She would have a natural desire to kill demons - Kalari/Ishanna used demons in her War that they fought in and they were created with a natural desire to destroy anything demonic or devil or from the Abyss - or similar places depending on the world. The dragon thing came from the time of the Firstborn, if I remember, so in truth, given how quickly these were created and thrown into battle, the fear/repulsion to dragon-kind is probably less in comparison, which will make them easier to live in the Nexus worlds.

The only way that would work is if she sensed they can be returned to the 'light' (good) or had bonded to them before their fall. They were thrown through time and space. Iarion did not go through time, but the phoenixes that founded Sentra were. How many years (or millennia) they were thrown is up to you. They could have also been thrown into the future if you want.
The amount of memory she has retained is up to you. Iarion (who lives at Treval) is clueless and the only home he remembers having is at the Dragonry's Library after resurrecting on Anarnedor. He doesn't know who created him, why, or have memories of the war (though probably has a form of PTSD that he has no idea where it comes from). The phoenixes who live/lived on Sentra vary with Thanar remembering everything and others bits and pieces, though many don't care anymore and devoted their time and energy to creating their new home.