The map number at the top of the page is used as a seed for the random number generator. The seed can be anywhere from 1 to 2-billion. Multiply that by three size and the combination of colours and tile types and you have a near-limitless number of options.
There is a hand made library of room designs as well as a set of simpler designs generated by the system. These are randomly selected for placement on to a grid, starting with the entrance. An algorithm then connects rooms together. The final step is to build the image using floor tiles and walls.
The original dungeon map generators used lower resolution graphics and different techniques to build the initial map.
There is a lot of large image manipulation that has to go on to make a map image. For the largest image size this can be hundreds of megabytes of data in memory. Processing that can take a moment, but good things come to those who wait.
Unfortunately not. The way in which the code works is part of the "special sauce" that makes Gozzys.com work. The good news is that you can reuse the maps that are produced under a Creative Commons license.