Of course, you can send Dai or any token from metamask wallet to other wallet or exchange as long as it has a deposit option for your coins. Also don't forget that metamask also needs Ethereum gas fee to send coins.
Yes, and as far as what I have used Metamask is still very safe and very comfortable to use in any transaction, including DAI token transactions, so I think this kind of thing has been done very often by everyone and doesn't need to be discussed repeatedly.