If I Detonate a minion with the Lethal ability, is the damage from Detonate Lethal?
No, the source of the damage is the Detonate spell itself, not the exploding minion.
What if I choose a Warded minion to destroy?
The Ward breaks instead of the minion being destroyed, but there's still an explosion. After the ward breaks (protecting the minion from the destruction effect), it will still take 3 damage along with the other units at its location.
