How to win with a “weak” Knight?

I'll take a look at the teleporters later, but Slagfest seems a bit unclear. Is a sulfur mine with a few resources really that necessary for a Knight? And capturing a Sorceress, and if possible, another Castle on day 8, would be great.
As for the Giants, I don't understand where to get the gems; you can't just play with a single unit. You need to somehow pit the computer-controlled units against each other.