I have played roleplaying games for decades but am confused about Fantasy Flight's take on Star Wars and can't find answers to basic questions I have. So hopefully people can help me here:
1) There are three core rulebooks from what I see. From reading reviews, I'm confused if these are all independent games that do not cross over ... or if they are just source materials that add to one core system that can be used in any time period.
2) Can I set a campaign based on any time period I want and have characters play whatever characters they want to? Or am I limited to specific types of characters depending on what rule book I use?

For example, if I bought the D6 West End version, it has rules that allow me pretty much to play in any era of Star Wars. The rules are the rules. From reading here, it seems to me like every one of the three rule books is a system upon itself that can't be used outside of that specific rule book. Any help is appreciated.

1. All three core books (the entire line really) is one system. All the books can be used. Pick and choose what you like. Include whatever books you can get ahold of.

The difference in the three is just in the theme.

The red covered books, Age of Rebellion, are themed around the rebels' civil war against the Empire. The white covered books, Edge of the Empire, are themed around scoundrels, pirates, bounty hunters, and the like. The black covered books, Force and Destiny, are themed around Force users.

2. With any of the core rule books, you can definitely run any sort of campaign in any time period you like. Of course, you're better off picking the core book and supplemental books that most match the sort of theme and campaign you want to run. But the rules and mechanics are the same throughout all the books.

There is a lot of fan-made material floating around that can help you put together bits and pieces for books that are hard to find these days. (I don't mean PDFs of the books. I would not know how to find those. They do not officially/legally exist.)

I hope that helps a bit. Please ask more questions if you like!

On the first question, they are all the same core system, with a few and generally minor tweaks/differences to account for the theme. As RLogue177 said, the red books focus on the Rebel Alliance and their fight against the Empire, the white books have more of a Firefly feel as they're about surviving on the fringes of society and skirting the edges of legality, and the black books are about exploring the mysteries of the Force and surviving in an era where Force users are feared, mistrusted, and to some extent outright hunted.

While all three lines are principally geared towards the Rebellion Era (aka the time frame of the original movies), you can run a campaign in whichever era you like. FFG has published sourcebooks for the later part of the Dark Times (covering the time frame of the Rebels series to just prior to the events of Rogue One) and the Clone Wars (primarily the Filoni series but also AotC and RotS). That said, I've played and run games set anywhere from a few years after Return of the Jedi to around the time of the sequel trilogy without having any major changes being required (for instance, most First Order tech and personnel are just Imperial stuff with an updated label, same for Resistance being Rebels under a slightly different name).

Now, it's hoped that if the game lines do continue (they're pretty much on hiatus due to corporate reshuffling at Asmodee's decree) that we'll see sourcebooks for other eras, such as the sequel era, early New Republic (aka around the time of The Mandalorian series) and the upcoming High Republic literary setting, amongst other Legends-based settings.