Hand of Fate. Part 2: Despair

Question: how to capture the first Castle with minimal losses? I do this in the 2nd week, but when capturing, they kill all the mages, half of the Gremlins, and part of the Djinns (there is no difference whether it's in Hero or Veteran difficulty, only more money is given at the beginning).

And how to get the Cold spell at the beginning? There are no Serfs to buy, and the chance of it appearing in the Mage Guild treasure chest on the way to the Castle is small, plus the losses are high.

What tactics does everyone use to replenish losses (again, at the beginning, 1-3 weeks)? I think I wasted my time developing Light Magic, as I still can't buy spells right away. Maybe it would have been better to develop Mechanics (and the Castle would be easier to storm), developing the Ballista and Tent?

Also, how to increase the chance of the Education artifact appearing at the beginning? I barely manage to get it by using the Mentor, spending all my money, which is unacceptable. With such a number of enemies, it is definitely needed.

Added 8 minutes later
I've been developing Chaos (Cold-Freezing Cold) + Logistics (Difficult Terrain) from the very beginning. What is better to develop as the 3rd skill? (1-2 weeks)