How does the Earthquake spell work, and why does it require mana?

Actually, there is only one tiny nuance. =)
It doesn't affect the standard spell because it doesn't deal damage to creatures. But in the machines branch, there is an "alternative" version that damages those behind the wall... and this formula is likely what the spell can affect. The only question is whether there will be even one player in the community who will choose "earthquake" in the machines branch instead of the ballista?

Oops... but this is much more interesting. It seems that "Lord of the Earth" does work, it's just that, as usual, everything is implemented in a clumsy way, and the developers decided to do it through some convoluted method. I'm too lazy to post a screenshot, so I'll just copy the text directly from the manual:

"Earthquake
The hero receives the "Earthquake" spell, which not only destroys walls but also damages and stuns all
creatures behind the fortress wall.
The damage dealt is equal to 10+5*Magic. Stunned creatures are pushed back 0.1 on the ATB scale. Units
of the hero that are behind the fortress wall also take damage"

So, it seems that "Lord of the Earth" was indeed created for this purpose. I WOULD like to say that, but while I was writing this message, I decided not to guess, but immediately go into the game and test it. In general, as Moonstar mentioned, and as Lorian wrote, "Lord of the Earth" doesn't give any bonus to the earthquake spell at all, in any version :D
But I discovered a very funny thing: when the earthquake deals damage to creatures, the damage log says "Silanna's wrath dealt... blah blah damage blah blah...", it's funny... well, we'll look for where the text for the earthquake's impact effect is and fix it, +1 text fix in patch 1.3 of my mod :D