Regarding MYSQL - the PHP approach described about will work fine, but in fact you can use any kind of sever-side CGI that you could with a browser. (For example, I generally write server side code in PERL for no better reason than I'm familiar with it.)
Additionally, I'm interested in the pipeline for combining art assets with the actionscript. My understanding is that art in a Flash project is more tightly integrated than in a typical C++ game (correct me if I'm wrong).
Art is typically embedded in the SWF at compile time (or even before), but it doesn't
have to be.
The reason it is normally done this way is because it keeps the delivery of the game nicely encapsulated in a single file.