Switching the game to cheat mode is very simple.
Exit to the main game menu (the title screen).
Type "unfrozen" in lowercase letters.
If successful, the word "cheat" will appear in the bottom-right corner of the screen next to the version number.
Next, load the desired save.
On the adventure map, press the "F2" button. The cheat panel will appear.
To disable cheat mode, you need to exit the game and restart it. Not very convenient if you just want to peek ahead at which skills were rolled at the University on a generated map, but play without cheats.
==========
How to control hero progression and spells in the castle (PVE, without cheats)?
I'm putting this knowledge in a spoiler, as this method requires a million saves/loads, and this knowledge is merely an unnecessary temptation. You've been warned.
Spoiler
Fortunately, each neutral army on the adventure map has its own "seed" (the seed for the random number generator), so replaying a battle after loading follows a predictable scenario. If you repeat the sequence of actions exactly, the AI behavior and morale/luck triggers are reproduced the same way. I like this. It was like this in Heroes 2 and Heroes 5. I call this genre "puzzle battles".
But hero progression and spells in the castle in Olden Era, alas, use random numbers from the common (global) generator. For example, if you have two heroes at the start of the map, and there's an obelisk granting 1000 experience near the castle, then the order in which you approach it matters: first with hero 1, then hero 2, or vice versa, first with hero 2, then hero 1. Different skills will be offered for selection.
My observations: visiting certain objects on the map (warehouses, etc.) and collecting resources also uses the global generator, so such actions affect progression. Interestingly, visiting objects like stables, fountains (+40 movement points) and wells also affects the generator. And importantly, the well in Olden Era can be visited as many times as you want per day — each time it fully restores mana (and generates a new random number for some reason).
Example: on the map "Mysterious Island" there is a well next to each castle.
Task: give a secondary hero the "Economics" skill upon the first visit to the obelisk.
Solution: stand next to the well, save, visit the obelisk. If you're unlucky, repeat until success: load, visit the well, save, visit the obelisk.
After all, this isn't a cheat, is it? It's a trick. And you can confidently say: "I beat the map without cheats." 🤞
P.S. By the way, bonuses from visiting different stables stack: each one gives +20% movement points until the end of the week.
UPDATE: The latest patch fixed the well "abuse", so visiting it no longer affects RNG. There's hope that the developers read this forum. Of course, I'd like heroes and towns to have their own seed (personal RNG), so that progression is as stable as in "Heroes 5", and spells in castles are fixed at the start of the map, rather than on the day the guild is built.