Isn’t 200 men too few to hold a castle the size of Harrenhal against a determined enemy? Also, why did Tywin leave all of his noble POWs at Harrenhal instead of taking them with him back West, where he could leverage them against their Northmen brethren he’s about to fight?

It is, but A. even 200 men would inflict significant casualties on an enemy before losing, B. Tywin couldn’t afford to leave a bigger garrison behind and fight a western campaign, and C. trying to escort large numbers of prisoners on a forced march through enemy territory is a great way to lose prisoners.