Are there any reasons the plague happens in towns, such as a prerequisite? (Bad hygiene, public health, etc) or is it just random? And can I die if I don't have a son and the plague strikes? Or are they really just that brutal? XD (Nah, I love this game A TON)

You can certainly lose if you don't have a son and the plague strikes you down. Not sure how the plague strike mechanics works though as I have not put nearly enough of my time into this brilliant game.

I've spent MANY hours with The Guild, and I can say quite certainly you can't prevent the plague from breaking out; even if you're mayor of the town, you can't invest in hygiene. It happens quite randomly.
And, like Ralackk said, if you have no heir over the age of 12, and your character dies of the plague, it's game over for you.

Try as I might, I just can't seem to die from the plague. People had fallen left and right, but my good ol' Jim Blacksmith was doing just fine. Played quite a few games, too. It looks more "set" than random, but perhaps it has a minimum time that must pass between two outbreaks.

Yes, I've also noticed a plague won't strike every other year, but other than that, there's no clear logic/system to it.