If I have all my SNGLS stored at Binance and they do an airdrop, is there anything I have to do to receive my ETH? And has there already been an airdrop? If so, when was that?
No there has not been an airdrop, there is a singulardtv blog article about binance supporting all future airdrops. But previously there were talks about need to invoke the claim function on the smartcontract. I did not read anything on binance Supporting this, so this is unclear still. This is that youn can store all the eth in the contract and claim the reward when you want. So its like an airdrop which you initiate.
So my best bet is to store them somewhere on your own wallet or singulardtv light wallet or singularx exchange as singularx has been confirmed from the devs to support this.