Here some ideas for re-edit (not re-write) the Prequels. I hope that this points solved some of the questions of the main message:
* At Ep1, Obi-Wan and Qui-Gon are both Jedi Knights and friends (not Master and Padawan). Both have been trained by Yoda.
* Not remove Jar-Jar Binks, but edit about 50% of his dialogues. Removed some scenes of the Gungan Battle.
* Maul is presented by Sidious as "Darth Vader" (that meaning "Emperor's Right Hand"). In some moment, we discover that Maul was a Jedi Apprentice that became to the Dark Side.
* Remove the scene of Anakin testing the Podracer. When Qui-Gon says: "I didn't actually come here to free slaves", the scene passes to Qui-Gon and Anakin watching the stars.
* When the droid army is destroyed, Maul (a.k.a. Vader) escapes. Qui-Gon is killed by Maul, but Obi-Wan not kills Maul.
* At Ep2, Dooku is replaced by Tarkin. The Clone Wars are the same, with no changes (only Dooku by Tarkin). Tarkin is allied with Palpatine all the time, but we only know this at the end of the Ep3: when Palpatine and Tarkin apparently sign the end of the clone war and the rise of the Empire, with Palpatine as the Emperor and Tarkin as the Main Governor.
* In Tatooine, when R2 reports the Obi-Wan's message from Geonosis, Anakin says to the Lars family: "Now the galaxy needs me. Maybe we can stop a war". And Ower says: "Don't go Anakin, forget that idealistic crusade. You have a home here". But Anakin will go.
* At the end of Ep2, Maul (a.k.a. Vader) returns and fights with Yoda at the end of the movie, and escapes too.
* Removed General Grievous and Anakin's Dream. Anakin goes to the Dark Side by lust of power (for example, command all the Republic Fleet) and by the wish of training his son in the Force ways (that is forbidden by the Jedi Council, like the marriage)
* At Ep3, Palpatine seduces Anakin and ask to fill the position of Maul. In this point, Anakin's intentions are not clear: Anakin saves Palpatine from the Jedi Council, but not joins him.
* Maul (a.k.a. Vader) leads the Clone Army in the Jedi Temple Battle, to destroy the Jedi Knights. Anakin and Obi-Wan go to fight him, apparently to save the Jedi, but Anakin starts to use the anger to fight Maul. In this point, Anakin is removed from Obi-Wan, in the face of Obi-Wan's wishes to stop the Anakin's anger.
* In the duel, Maul (a.k.a. Vader) apparently defeats Anakin, but the resolution of the duel is not seen. We only see Obi-Wan regretting what happened, and fleeing with Padme.
At Ep5, we discover that Anakin defeated Maul and he converts in Darth Vader or the Emperor's Right Hand.