A battle with indestructible still loses defense counters as it's dealt damage. If it's a Siege, it will still be exiled when the last defense counter is removed from it, and its controller may still cast it transformed without paying its mana cost.

A planeswalker with indestructible still loses loyalty counters as it's dealt damage and will still be put into its owner's graveyard if its loyalty reaches 0.

The set of permanents affected by Heroic Intervention is determined as the spell resolves. Permanents you begin to control later in the turn won't gain hexproof and indestructible.