Oh. Does it ever say why Midian is after Jeruh?
In Jeruh's cell Midian revealed how he survived the Landorin Massacre after seeing Jeruh kill Serena and he swore revenge, we can only assume thats what Rhue was doing when he under the Midian persona.
1. There was a flashback scene where it showed Rhue talking to a young Lyrra, and, according to the scene, Lyrra was his daughter. Lyrra was afraid because something happened to Jeruh. The scene was dark and stormy. What was that about?
This was right after Rhue killed Jed, and he was experiencing one of Jed's memories from Jed's point of view. It was right after the Landorin Massacre and Lyrra saw Jeruh kill everyone and pretty much blocked it all from her mind.
2. So we don't really know who Rhue truly was? His "original" self and for how long he has been alive? That is all a mystery.
Quick timeline of what we can reasonably assume about Rhue's various identities:
original identity -> ...unkown... -> Kura -> Kava -> ...unkown... -> Midian -> Jeruh(Rhue)
All we know about his age is that he's been around for a long time, as mentioned by the PS and guessed at by Gaius. As for who he is, well the best guesses are he is the son of the Lord Below, and it takes a small book to even begin to explain how anyone came to that conclusion, suffice to say it involves the attack on the LotP by the Illuminati and the demise of Janwen and the side effects of the Lord Below's desperation attack that just 'decimated the auras' of the entire city. Basicly go to the room where you find Lexus and theres a bookshelf with 3 poems, describing 'The Mimic', 'Venge', and 'Kura'. Since Rhue was at point Kura, and the Mimic poem pretty accurately describes Rhue, its not a stretch that all three poems are all about Rhue, with Venge as his origin. So check those out.
3. What caused Rhue to kill all those people throughout his different lives/memories? Did the Shadow Sword turn him evil? Was it just casual killing such as bandits who attacked him? Was the sword acting on it's own? I assume it's just the same as his current "Rhue" life, just killing for whatever reason like he did during the game.
We don't know much, but its pretty clear that the sword wants Rhue to kill as much as possible. How picky it is about who it kills has had much debate (the reaches ending is a good starting point for this), but in general the points when it switched auras on Rhue were at points when its current aura were at the verge of becoming much less likely to be killing again and it had just acquired a new aura that had plenty of reason. As for motives again I'd point you to the reaches ending.