1: Jedi don't like evil. They're entirely 'ANY EMOTION IS A BAD THING. >
' Not to mention that there were... Two Sith compared to hundreds of thousands of Jedi. Not really... Balance. More... An army of people trying to be worse than droids against two guys that are like 'Wooo! Evil!'
Vader brought balance to the force by leaving Luke as the only Jedi left. A Jedi with knowledge enough to let future Jedi have emotions rather than detach themselves from the rest of the galaxy and try to be droids. All the stupidity of 'Jedi cannot love, because love can bring the dark side' was removed... A true Jedi knows how to control their emotions instead of cutting out their humanity/sanity/whatever.
2: The Sith that had been playing the ENTIRE GALAXY and twisting everything for a good part of the past few decades, certainly the past three years for the clone wars.
This is like asking 'Hey, do we keep this guy who's responsible for the death of UNTOLD BILLIONS alive? He'll probably try to kill us or escape if we blink...'
It's not like the Jedi have had a good field record with keeping prisoners alive. Like... Oh. Jango Fett, Count Dooku, General Grevious, Sev'Rance Tann, Cydon Prax, Durge... And more.
3: Technically not. Darth Bane (Which was... Uh, about a thousand years before episode 4 if I recall correctly) basically went 'You know what? Sith REALLY hate each other and do stupid things... Like backstabbing one another. We should hide. So, there'll only be master and apprentice. Only two in the entire galaxy. That'll make us hard to find.'
BUT. The emperor and Vader still trained and made use of dark force users. People such as Jerec and his crew of 'sith' or Lumiya and her eventual turning of Jacen Solo into Darth Caedus... Not to mention the rebirth of several ancient Sith (Such as Freedon Nad)
Still. They were arguably not 'True Sith'. Indeed, it's entirely logical to argue that Vader was not a Sith... The emperor never taught him Sith Alchemy/magic or the dark ways of the force, instead opting to let Vader just limp around and use his pain/anger to fuel himself.
EDIT: Well. Okay. Darth Krayt still existed later on due to the magic of stasis. He'd be the last 'True sith' before training his followers. Mainly thanks to Krayt's study of holocrons left by the actual Sith (Such as Darth Nhilus). Still. That's 120-something years after episode 4. Quite a long time.