>1. Is there a class where it takes an audio file as a constructor and has methods that allow me pause, play and continue from any selected part of the song?
According to API ackage javax.sound.sampled provides interfaces and classes for capture, processing, and playback of sampled audio data. However I never used it...

>2. How do you get video to work on an applet and have the functionality from question one?
You will have to search on the matter, but maybe you should read this first...

>3. How do I fade an image to a particular color?
Original Java image functionality is limited. However, Sun Systems seen this problem and support many community projects which try to solve the problem. To address the issue there is a Java Advaced Imaging (JAI) and Java Advanced Imaging Image I/O Tools API Core (jai-imageio-core)

>4. What would you say is the max refresh rate for a 1680 x 1050 applet with double buffering and without any choppiness? (considering that I'm using an up to date computer).
That image size is to big, it will take hell of time for processing and downloading for users. Just look what is the size of videos posted on youtube, google or yahoo videos

>4b. If simply took a small image and stretched it to 1680 x 1050, would it change the fame rate?
Now you lost me... Do you want to stretch video of small size to larger view or you trying to use images and get video out of it???