I'm new to this ActionScript language, however I have 2 questions.
So you code in ActionScript (2 or 3) in Adobe, and then export it as a (I believe) a .swf file, which you can upload to newgrounds or something as a game? I would like to know if this is the process? Or if that is not, what is the process?
Have there been any bigger-name games that were developed with ActionScript? I know most games are parsed over to different languages.
1) Yes, that sounds about right. You code in AS2/3 (I like 3) and compile/export to a swf. That swf is an "executable" that will run in the Adobe Flash Player. That swf may rely on external resources such as sounds and images, or they can be packed inside the swf. I'm not sure about newgrounds' process, but in theory if you pack the resources into the swf you should be able to simply upload the swf and be done.
2) There are more flash games on the web then you could ever begin to count. Newgrounds, miniclip, and similar sites are good places to start, but web based games are not the only flash games. Flash games can be packaged as standalone PC games and even as iOS and Android apps. As far as big-name games, that really depends on your definition of big-name. Farmville is a huge multi-million dollar revenue game made in flash. The original Super Meat Boy was done in flash, though I think the retail version was redone in something else. Flash/AS3 is pretty powerful and totally acceptable for big-name games, as long as your game is actually good and you avoid/workaround a few of flash's drawbacks.