Off the Island
Are there still any questions about Eloise? I think all the mystery surrounding her has been lifted away. I may be the only person who believes that though. Here’s how I see things.
Her all-knowingness in the flashbacks and off the Island
People still ask how she knew stuff to say to Desmond in Flashes Before You Eyes I’m pretty sure she knew so much about time travel because she had Daniel’s notebook and she probably spent all her life trying to understand it. She likely also saw the part about Desmond being Daniel’s Constant so she kept track of him, when the time was right she made sure he didn’t try any funny business. Of course she was wrong about him, but that’s irrelevant.
Her knowledge in the flash-sideways
This one is a lot easier to explain. Evidently Eloise was one of the first people to flash. She remembered all that she did in her last life, and she remembered what happened to Daniel. Therefore, it looks like she devoted her entire life to his happiness. She wouldn’t let anything interfere with his happiness , not even his own self-awareness or love. She was pretty much living out her own fantasy and she didn’t want Desmond screwing it up.
At some point Daniel would flash, likely when he’s around Charlotte some more. I’m not really sure why the writers didn’t want that to happen in this episode.