1. Two secondary castles are captured by the main hero. Is this a rule (to get 500 experience for capturing a castle), or a fear of easy blockades on the roads, or simply Kiryu had nowhere else to go, or something more complex?

Kairi went to the Barbarian secondary castle with the intention of leveling up her archery to expert, using it to kill the griffins guarding the lair, and then taking the lair itself. However, there wasn't enough money to hire unicorns/dryads, so the lair wasn't taken... But experience was still gained from the griffins.
He went to the swamp mostly because there wasn't really anywhere else to go. He didn't feel like rushing the gnome/medusa stacks on the first map, and there wasn't anything else valuable visible on the map.

2. On day 113, a gnoll was dismissed, even though a raid on the swamp was planned. Is this a mistake or an attempt to save money?

I usually buy heroes for gathering resources in the city where there are many gnolls available. It's usually not possible to send an extra gatherer from the start. And there's no point in taking a gnoll with the main army just to save a few gold coins - it's better to have +1 morale in case of a blockade.

3. On day 121, Deemer's wisdom was increased instead of basic literacy - why?

I didn't have any plans for Deemer, I just took him automatically.

4. The battle in the nagabanks - was it worth going there at all? What is more valuable - the lost army or 8000 gold? Or was there an expectation of fewer losses?

Before this battle, the game crashed, so I played poorly here. The battle itself seems to have been conducted poorly; I should have taken different troops and positioned them differently... I was hoping for minimal losses - a few units and maybe a few centaurs... At first, I felt bad about the army, especially since by that point I already had more than 5000 gold and everything was bought - it seemed like I didn't need gold - but at the beginning of the third week, I started to run out of money, so overall - it's tolerable.