Can I play Abandon with nothing on the stack?

No, you cannot play Abandon if there is nothing on the chain.

According to RiftJudge FAQ #9981 and Rule 4070, because Abandon requires a target ("Counter a spell"), you must have a legal target available on the chain to put the spell on the chain in the first place. If there are no spells on the chain, there is no valid target, and you cannot play the card.