Full analysis
ACR’s passive counts debuff types, not individual debuffs. If her Login SPEQ applies a Damage debuff, her active Skill’s Damage debuff won’t increase her Damage as they’re the same debuff type.
ACR's Login SPEQ says it applies "3 random debuffs", but the actual debuffs are divided into groupings, and it applies 1 debuff from each grouping.
- DMG or RoF
- EVA or ACC
- MOV or ARM
As such an enemy can never get a Damage AND Rate of Fire debuff from this, but can get Damage, Evasion and Armor for example.
ACR’s passive stacks additively. So with the 3 debuffs from her Login SPEQ, she will have 20% (10% + 5% + 5%) increased Damage. This effect increases her auto-attack damage multiplier while her target has debuffs. It is also not Final Damage (so it is before enemy Armor).