QFor the "-10 damage" of hBP02-100〈Knight's Order of Shirogane〉, if an Arts deals both special damage and damage, does this get applied to both and result in "-20 damage"?

AYes, this -10 is applied to damage dealt by ability as well.

QFor the "Deal 10 special damage to your opponent's center holomem for every 10 HP restored." of 《Bloom Effect》 "Seductive Gaze" of hBP02-060, if the target for dealing damage is 〈Shirogane Noel〉 with hBP02-100 "Knight's Order of Shirogane" attached, do the multiple instances of 10 damage dealt get reduced by 10 and result in 0 damage?

ANo, for this ability's damage, if "50" was restored, "50" special damage will be dealt in one go.
If the target is a holomem with hBP02-100 "Knight's Order of Shirogane" attached, and "50" was used as the example, the "-10" is only applied to the final damage of "50" and will result in "40" damage dealt.