The republic slowly did come back after he was killed. It was almost destroyed several times, but in the end they managed to secure victory. Its too many countless tales, books, and comics for me to go into detail. but the sheer volume of litterature form that era assures me a great deal of people worked to bring it back. Not just spring back magically, like you say. A two hour movie is only so long, we can't follow series upon series of characters all doing things adding up to the collapse of the Empire. Would litteraly be an eternity worth of stories, by any human standards. When I say the Star Wars fandom is huge, I mean it.
Finally someone else on these forums who has read the Star Wars books, I'd have to say that this is the universe I am the biggest nerd about. I personally think that Darth Sidious and Darth Vader were inferior compared to some of the Sith who came before, notably Darth Bane and Darth Zannah.
There are well over a hundred books set in this universe spanning from 5000 years before the Battle of Yavin(BBY) to 43 years after(ABY) and that's not including the comics.
So why didn't he find Vaders son when he was just a baby and be done with the whole thing? Seriously, he controls a whole Galaxy and has the power to influence pretty much everyone.
Why does he even need a Death Star? Just get a hundred ships to blast the living crap out of the planet from orbit.
Just seems stupid that a Galaxy wide Empire is defeated by Ewoks.
Also I am talking about the movies themselves. I know there are books and comics and so on. But the movies themselves make no sense at all IMO.
He didn't find Luke because he was being hidden by two powerful Jedi Masters and the galaxy in Star Wars is a damn big place. http://www.starwarsmap.com/official_star_wars_galaxy_map_picture_image_photo_pic_pix_photograph/star_wars_map_star_wars_galaxy_map_official_galactic_map_star_wars_universe_1.jpg shows just some of the better known planets.
He wants to build a Death Star as a terror weapon, Tarkin explains this in Episode IV. Saying you have a fleet that contains thousands of powerful ships that could burn entire continents to ash is a bit less intimidating saying you have a moon sized space station that could completely destroy a planet.
The Empire wasn't defeated by Ewoks, what happened in Episode VI was the destruction of the Death Star, the deaths of Palpatine and Vader and a portion of the Imperial fleet. The Empire was never really defeated in the books, it just became smaller with less influence and eventually signed a treaty with the New Republic(Rebel Alliance).