When you rest it heals strain according to your endurance then heals damage with any excess points of Endurance. I'm wondering if you have no strain can you rest and heal according to how much endurance you have?

Yes.

Yes. There is no prerequisite of having suffered strain to use any recover strain ability.

Any recover strain ability recovers damage for each strain not recovered. (Includes but is not limited to a hero spending upto one surge per attack to recover 1 strain.)

But note that it has to be recover . If an ability allows to remove strain tokens, it does not allow to remove damage.