NHF – new heroes for Heroes V 3.1.

If there are only 6 skills available in school, and their appearance doesn't repeat consecutively, the randomness will be small (but is it really?).

The randomness will be high (higher than it is now) in any case. And what does "doesn't repeat" mean? The same perk can be offered multiple times; it seems you haven't leveled up in a while, considering you're suggesting ideas that would not only eliminate the ability to level up properly but also the ability to level up effectively as a whole. :)

As for me, there's nothing beautiful about it. When it's illogical for one skill to lead to another.

Well, everyone has their own logic, but the structure itself looks better than complete chaos (without any connections at all).

As I understand it, when leveling up, the game doesn't care whether it's a third-level perk or a second-level perk that's being used for leveling (the difference only matters between levels 1 and 2/3).

Yes.