MMH5.5 - Heroes of Might and Magic 5.5

How are you going to cope with shatter perks that increase the mana requirement by a factor of 2?

Obviously, they need to be weakened to 1.5 (as it was in the original). You strengthened these skills because knowledge in long games wasn't playing half the role it should have.
Meanwhile, with the right balance, a 1.5x price should correspond in strength to a -33% SpellPower penalty (in both cases, the parameter is effectively reduced by 1.5 times).

how much damage will "Meteor shower" have as a base and how much will be the spell power increase?

If the current multiplier is 20, then roughly - 30. That is, the same formula N*(Spellpower + 1), but with a multiplier of 30.
But it could also be 25, it needs to be tested.

Added 5 minutes ago

I saw it and some of the changes (Haste, endurance) will make might heroes overpowered as their mana price is affordable and the flat boost is high.

1) Haste was weakened, not strengthened (no bonus from SP).
2) Endurance and Righteous Might are cast on a 4x4 area, not on all troops (besides, Endurance is not very useful against Magic, and Righteous Might is twice as expensive and costs 40 mana).
3) the duration of the spell = 1 + 0.2 * SP (while SP < 10 for a warrior, this is a weakening).
I wrote about all this.

This way Magic hero with Light will compensate the stat difference when he fights against Might classes.

Have you seen the bonuses for Endurance or Righteous Might? 50% of SP goes into the parameter, not a paltry 10-15%. It is precisely due to these spells that Magic classes can convert their SP into attack and defense if given enough time.

Added 7 minutes ago

If this artifact stat is in the exe file then we cannot do it. Probably some other negative effect will be added.

Penalties won't help much here.
-1 to morale is nothing (especially for Magic classes, and there is no penalty for the necromancer).
Either you will have to penalize all parameters at the same time (for example, -4 to all primary hero parameters and a price of 40k).