1. Why do you boil the wort after mashing? What is happening in that process?
Sanitizing the wort. Protein coagulation. Some maillard reactions in the malt. Isomerizing alpha acid (making the beer bitter). Lot's of stuff...
2. Some beers --like Flemish Reds-- say to age for many months, sometimes over a year. Does this mean just keep it in the secondary for that long, topping off the airlock once a week or something and letting it sit there?
Yup, that is basically it. Depending on the aging period, it isn't always 100% necessary to use a secondary vessel to age.
3. Does software exist wherein you can plug in information about your water (that you can get from your municipal water supplier) and it'll tell you what you should do to treat your water properly?
Most brewing software has some sort of water functionality. I use the 'EZ Water Calculator' Excel spreadsheet which is free.
4. What tricks are there to reduce DMS production in lighter beers other than a 90 minute boil and rapid cooling of the wort?
Those are the main ones. You can avoid lightly kilned base malts (like pilsner malt) that have higher levels of DMS precursors.