Formulas and Game Mechanics

Damage Formula
The damage output for a normal attack is: $$ \definecolor{bg}{RGB}{47,22,2}\pagecolor{bg}\definecolor{let}{RGB}{255,195,86}\color{let}{\text{DMG} =  \text{ATK} \times E \times A \times D }$$

$$ \definecolor{bg}{RGB}{47,22,2}\pagecolor{bg}\definecolor{let}{RGB}{255,195,86}\color{let} E $$ is a modifier that depends on element of attacking hero and the target, for more information, see The 5 Elements. $$ \definecolor{bg}{RGB}{47,22,2}\pagecolor{bg}\definecolor{let}{RGB}{255,195,86}\color{let} A $$ is attack modifier that affects the Attacker. $$ \definecolor{bg}{RGB}{47,22,2}\pagecolor{bg}\definecolor{let}{RGB}{255,195,86}\color{let} D $$ is attack modifier that affects the Defender.

The damage output for attack skill is: $$ \definecolor{bg}{RGB}{47,22,2}\pagecolor{bg}\definecolor{let}{RGB}{255,195,86}\color{let} \text{DMG} =  \text{ATK} \times E \times A \times D \times C \times P $$

$$ \definecolor{bg}{RGB}{47,22,2}\pagecolor{bg}\definecolor{let}{RGB}{255,195,86}\color{let} C $$ is a modifier that depends on Number of Charges of the skill (explained with more details below). $$ \definecolor{bg}{RGB}{47,22,2}\pagecolor{bg}\definecolor{let}{RGB}{255,195,86}\color{let} P $$ is the Power of the skill.

The damage output for skills that have "for X secs, health decreases X% of Atk" (ex.: Thousand Swords, Holy Cross): $$ \definecolor{bg}{RGB}{47,22,2}\pagecolor{bg}\definecolor{let}{RGB}{255,195,86}\color{let} \text{DMG} =  \text{ATK} \times E \times A \times C \times P $$

Note that Buffs or Debuffs on Defender are not applied in formula above, and the damage changes if Attackers attack is increased or reduced in middle of skill effect.

The damage output for healing skill is: $$ \definecolor{bg}{RGB}{47,22,2}\pagecolor{bg}\definecolor{let}{RGB}{255,195,86}\color{let} \text{DMG} =  \text{ATK} \times A \times C \times P $$

Element Advantage/Disadvantage Modifier is not applied for Healing.

Buffs
The [Buff] denotes 100% summed of all attack modifiers on the attacker. For example, if Yun is receiving +150% atk increase from Raven, then [Buff] = 1 + 1.5 = 2.5. If she receives an additional +125% atk increase from Ein, then [Buff] = 1 + 1.5 + 1.25 = 3.75.
 * Some Characters with [Buff] skills are: 4-6* Ravens, 1-6* Eins, 5* Freya.
 * Character Leader Skill such as "Damage 30% increase for all servants of same element" is also [Buff] type.
 * Guild Damage Increases (such as Guild Raid damage 20% increase) is also [Buff] type
 * Element Advantage (this seems to change depending on game version, Fantasia heroes seems to have different mechanism here)
 * "When Attacked Dmg % Reduce" Leader skill is also Buff

Debuffs
The [Debuff] denotes 100% summed of all damage/defense modifiers on the target. Another example is if the target is receiving "when attacked damage 100% increase" from Caesar, then [Debuff] = 1 + 1.0 = 2.0. NOTE: Those debuffs don't affect skills that have prolonged duration like Freya thousand swords, Diana's Holy Cross.
 * Some Characters with [Debuff] skills are: 5-6* Caesars, 4* Yun, 5* Girtimuka.
 * Element Disadvantage (this seems to change depending on game version, Fantasia heroes seems to have different mechanism here)
 * There is a bug that makes Caesars debuff don't stack on each other, so double Caesar is useless. However, Caesar and Mac debuff stacks.

Critical Hit
For critical hit its:

$$ \definecolor{bg}{RGB}{47,22,2}\pagecolor{bg}\definecolor{let}{RGB}{255,195,86}\color{let} \text{DMG} =  \text{ATK} \times (E \times A \times D) \times C \times P \times R $$ $$ \definecolor{bg}{RGB}{47,22,2}\pagecolor{bg}\definecolor{let}{RGB}{255,195,86}\color{let} R $$ is the Critical Power of the Attacker.

Skill Charges Multiplier [Charges%]
For attack skills, on first charge character gets 100% damage, on subsequent charges, damage percentiles are increased by 140%. See table below:

In contrast with Celestia, Fantasia Heroes have the following table for Girtimuka's Debuff. Also, Girtimuka debuff is applied per entity and not per tile: