If a creature takes non-lethal damage, turns into a non-creature, and then back into a creature, does the damage remain?
Yes, Damage is marked on a permanent even if it is not a creature.

Comp rules:


  119.6. Damage marked on a creature remains until the cleanup step, even if that permanent stops being a creature.


Heliod will also not be indestructible in the given scenario, since he was a creature while Hour of Devastation was resolving, which is all that HoD cares about. Changing or losing permanent types does not cause Heliod to regain indestructibility.