Can I use Zebstrika's "Sprint" Ability if I have no cards in my hand?
Yes, since you can have a hand of zero cards you can use Sprint as long as there are cards in your deck to draw from.
Source: TPCi Rules Team (2019-03-21)
Can I use Zebstrika's "Sprint" Ability to discard my hand if there are no cards left in my deck?
No, you cannot. Discarding your hand is a cost not the effect, and you cannot use Abilities for no effect.
Source: TPCi Rules Team (2019-03-21)