Can you use an exchange wallet address or do you have to use their wallet to receive the airdrop?
For you good, you'd better use the address generate with the deeponion's proprietary wallet. So you can own the private key of the address and fully control them.
But CAN you use exchange address instead?
I don't think this is advisable. You will receive the coins at first in the address provided by the exchange, but the exchange will 'manage' and move the coins themselves to another address. I can tell this because I tracked my btc address in exchanges through block explorer and I was surprised that a few moments later, blockexplorer says my address balance is zero but I still have the balance in the exchange. I read somewhere how exchanges manage the users' coins that in exchanges we are only trading with numbers and not with the real coins/tokens. So what will be left for the user balance in exchange are numbers provided by the exchange and not the real coins. They only will credit back the coins to your personal address once decide to withdraw.