If Ezreal - Dashing has Spellsong, does he deal his attack damage twice? Can he select different units for each attack?

Yes, Ezreal, Dashing equipped with Svellsongur will trigger his "When I attack" ability twice, and he can select different units for each trigger.

The Ruling

When Svellsongur is attached to a unit, it copies that unit's text. Because Ezreal's ability is a triggered ability ("When I attack..."), both the original ability on Ezreal and the copied ability on the equipment will trigger simultaneously when he attacks.

• Two Triggers: Both abilities trigger when Ezreal attacks. They are placed on the chain, and each will resolve individually.
• Targeting: Because each trigger is a separate instance of the ability, you choose a target for each one as they are placed on the chain. You are not required to target the same unit; you may choose two different enemy units at the battlefield to deal damage to.

Sequence

1. Attack: Ezreal attacks.
2. Triggers: Both Ezreal's native ability and the copied ability from Svellsongur trigger.
3. Chain: You place both triggers on the chain. You choose a target for the first trigger and a target for the second trigger.
4. Resolution: The triggers resolve one by one (LIFO). Each deals 3 damage (Ezreal's Might) to its respective target.

Note: As per Ezreal's card text, he does not deal standard combat damage during the Combat Damage Step; he only deals the damage specified by his triggered abilities.