Unique skills and abilities of heroes.

Answers to all questions in order:
1. The GUARDIAN spell! What is its principle of operation? Does my hero simply counterattack the enemy unit that attacked the unit being protected? If so, how is this better than simply attacking with the hero instead of casting the spell?
The essence of the Guardian ability: The Knight gains a special combat skill to protect one of his units until the end of the battle, dealing damage to enemy creatures attacking that unit.
This is better because when calculating the hero's attack, his attack is increased by 3.

2. The INSPIRATION spell! The description says that it increases the chance to move by 33%. That's clear, but... how many turns does it last? If it only lasts for one turn, then there's no point in casting this spell on a unit that moves immediately after the hero (it will still move next, and the spell only lasts for one turn).

This is not a spell at all. It's a perk from the Leadership skill tree, which gives the ability to use the Inspiration spell. The unit moves forward 0.33 on the initiative scale, but, of course, not beyond its beginning (if the unit was on the scale at position 0.68, or closer to the beginning, part of the effect will be lost).

3) Is there any information available about the additional abilities of units? I have an idea to learn the SOLDIER'S LUCK spell. But what's the point? I don't know which units it could even apply to! Maybe I don't even have any of those units!(!

Storm (two attacks per turn) - Landlords
Stun (reduces initiative) - Peasants.
Stunning Strike - Swordsmen, Halberdiers. (This is about Haven, so only these units)

4) So, here's another question (in addition to the previous ones): if a unit is attacked by archers or mages, and the GUARDIAN spell is cast on the unit, what happens then? Will the hero counterattack?

Archers attack, mages who cast spells do not attack. But if they just shoot, then they attack.

5) There is a skill called FUNDAMENTALS OF MAGIC. It says: "increases the speed at which the hero casts spells in battle"! And that the interval between two CONSECUTIVE spells is reduced by...
I can't figure it out. Does the hero start moving more often? Or how should this be interpreted? Or does it only mean that when he casts a spell, his turn comes faster?

The hero starts casting spells more often, that is, when casting a spell, his next turn will come faster. But if he uses a simple attack on the next turn, he will not receive a bonus to his movement on the initiative scale.

5) How far from the True location of the Tear can you dig to find it? Does anyone know?

Three squares.