You can have up to 5 simultaneous games going in the Windows version of Fish Tycoon. This thread explains how to start new games (either starting over or creating additional players), complete with screenshots.

As for the music that occasionally plays, it came to be known as "mystery music" during the Fish Tycoon for Pocket PC beta. It drove me crazy until I figured it out. Arthur prefers to preserve the mystery surrounding that music, so I won't spill the beans here again.