If you want to write Flash (although I don't consider entire sites written in Flash to be websites: websites are written in HTML, CSS and Javascript) then just learn Flash/Actionscript. It's almost certainly simpler than Java.
To be honest I have no idea: I've never bothered investigating it as I have no interest in Flash. If you want a good base in understanding how to program I'd personally suggest a procedural language like C, then an OO language like Java or Objective-C. If you can understand C then you are that much closer to understanding how the computer actually works.
I suggest checking out http://processing.org to get started with programming -- it's like java but with training wheels and optimized for making very immediately visual programming experiments. Plus there's a great community online and a lot of documentation. All free. Good luck.
In my personal opinion, yes. I think that understanding how the machine works and that close to the metal feel of C is important. But many others will tell you that Java with it's garbage collection and inherant "safety" is a better first language. Either way you will be facing a very steep learning curve if you are doing this on your own...
My opinion is that learning one thing doesn't ever harm you when you want to learn some other thing, as long as you keep an open mind to doing things differently. So don't be afraid to try a few different languages and see how it goes. It's going to be difficult on your own, but it's possible if you can maintain an interest in it.