If I move damage from one of my characters this turn, does that cause Isabela’s Do No Wrong ability to trigger?
Yes. Moving damage counts as removing damage. You first remove the damage from one card in order to put it on another.
Official set release notes — Wilds Unknown
If I remove 2 damage from one of my characters, will I resolve Isabela’s Do No Wrong ability twice?
No. The ability triggers only once, no matter how much damage was removed. You’ll gain lore equal to the damage removed.
Official set release notes — Wilds Unknown