Discussion about the Sanctuary faction.

I read that Sacred Kirins have the highest initiative...

I meant the faction as a whole (get used to it, Sanctuary is often simply called Nagas, even though there are only two types of units). :) But you are absolutely right – Sacred Kirins have the highest initiative (60) in the game, along with the Void Worm (leader).

I just wanted to know in more detail how magic power and magic defense affect the attack of the troops themselves, and whether they affect it at all?

The attack power of units that deal magic damage is affected by your hero's "Magic Power" stat. This stat increases as the hero gains levels. You can also speed up the development of "Magic Power" by learning the "Guardian of the Secret I," "Guardian of the Secret II," and "Guardian of the Secret III" skills. Since we're talking specifically about Sanctuary, here's a list of creatures whose attack becomes more powerful with the aforementioned skills: Coral/Pearl Priestess, Stream Spirit/Mizu-Kami, Snow Maiden/Yuki-Onna. In addition, the "Magic Power" stat has a significant impact on the effectiveness of almost all spells (of any school) and magical abilities of warriors. This is extremely important for Nagas, as it provides a chance to upgrade "Wave of Refreshment," "Power Jump," "Ice Shards," and "Hailstorm." Now, about Water. Choose the "Water Magic I," "Water Magic II," and "Water Magic III" skills. Result: spells of the Water magic school become stronger (including some special hero abilities that depend on the Path of Blood/Tears and are based on Water), and the effectiveness of the four aforementioned unit skills increases. It should be noted that "Water Magic I," "Water Magic II," and "Water Magic III" do not affect the attack of creatures; the bonuses are only given when using spells/abilities based on Water (the same applies to all other magic schools).

How does it affect spells like Dominate, Summoning of all types of elementals, Time Stop, Ice Wall, etc.?
And why do they say that Ice Wall cannot be pierced by arrows, but in fact, arrows pierce it?

Regarding "Dominate" and "Ice Wall": it is impossible to influence the effectiveness of these spells; their effect is stable and independent. As for the penetrability of "Ice Wall," I can't say anything; I've never encountered this. But here's what I'll say about summoning: the number of elementals that appear is affected by the same "Magic Power" of your hero (and, accordingly, "Guardian of the Secret I," "Guardian of the Secret II," and "Guardian of the Secret III"), as well as the level of development of the magic school that you are going to summon, for example, the number of Water elemental units will be greater if you have learned "Water Magic I," "Water Magic II," and "Water Magic III."

Added 4 minutes ago
Yes, about "Time Stop." The higher the hero's "Magic Power" and the more advanced the Prime magic school, the longer the target enemy unit will be removed from action. But, as far as I know, the maximum is skipping three turns.