So I fast travelled back to my newly built house and appeared right in an ambush of 3 bandits who apparently had a pet dragon they brought along. Long story short, my housecarl, steward and I fended them off. However, the steward was killed.

I didn't want to mess around so I reloaded a save. But I was wondering, what happens if the steward dies? Can you replace them? If anyone knows, then thanks in advance.

My advice is don't fast travel to your house. Or take a carriage to it or near it. It greatly increases the amount of attacks you're going to get on your home, I'm not sure about replacing your steward, surely you must be able to. They must have foreseen them dying with the frequent attacks.

Ah, those pesky dragons. Skeevers are easy to kill, and giants are actually great training tools (you can level up Block, Armor, and Restoration just by rumpusing with a giant), and can be sneak-attacked if you're not in the mood to train. Dragons are another story.