Gleeful Arsonist's first ability resolves before the spell that caused it to trigger. It resolves even if that spell is countered.

If Gleeful Arsonist is no longer on the battlefield when its first ability resolves, use its power as it last existed on the battlefield to determine how much damage it deals.

Once undying returns the creature, it's considered a new object with no relation to the object that it was. Auras that were attached to it won't return to the battlefield. Equipment that was attached to it will remain unattached. Any counters that were on it won't be put on the new creature.