If I defend with Ezreal dashing, can I use his ability damage and also use his action to move him to base, killing a unit and retreating?

Yes, you can both deal damage with Ezreal, Dashing's triggered ability and use his activated ability to move him to your base during the same combat. Because the triggered ability and the activated ability occur at different times in the combat sequence, they do not conflict.

The Sequence

1. Combat Begins: Ezreal, Dashing is designated as a Defender.
2. Triggered Ability: Ezreal's "When I defend" ability triggers and is placed on the initial chain.
3. Resolution: The initial chain resolves. Ezreal deals 3 damage (his Might) to the targeted enemy unit.
4. Open State: Once the initial chain (containing the "When I defend" trigger) has fully resolved, the game state becomes OPEN.
5. Activated Ability: Because you now have focus in an open state, you may activate Ezreal's ability to move him to your base. This ability is placed on a new chain. Once this chain resolves, Ezreal is moved to your base.

Summary

You successfully deal the damage from his triggered ability first, and then you are free to use his activated ability to move him to your base. Since the damage has already been dealt and resolved, moving him to the base afterward does not negate the damage he dealt.

Note: I could not fully verify this ruling against the retrieved rules.