Metamask is a place to store assets that we have, and can be used to store more than one asset. but to make swap transactions to get a drop, usually it can only be used once. and if you want to get another drop, then you have to use another wallet..
We are not store anything on metamask, we just unlock our wallet by providing the key, so we can interact with our assets on the blockchain. All our assets are on blockchain, not in metamask or another wallet interface.
This is true technically speaking. But his statement is not wrong either because you will need to input your recovery seed on metamask which means you are entrusting all your funds store on that wallet address to them. So basically you are storing your funds on there wallet app since you give them your keys.
I think the reward will base on the address that use to swap on there exchange. The purpose of there airdrop if there will be is to reward user that used there exchange. So using different wallet in different Metamask might give you an edge to receive more rewards but still this is just a speculation and obviously there's a risk on doing it.