Can we backup our coins on MCW? Do I get a private key?

You can transfer your coins to your own hardware wallet if you’re wanting to keep them safe with yourself although MCW is covered by insurance if a users account was ever to be compromised within our system. If you're still wanting to transfer your coins to a hardware wallet - we recommend Nano Ledger S -

Do I get a private key?

myCryptoWallet is a hosted wallet, it's not feasible to provide the private keys to individual wallet addresses; doing so would prevent us from taking advantage of our cold-wallet storage technology to protect users funds to the highest degree. You can create new addresses for your wallets and these are yours forever. No matter how old your wallet transaction address is, you will still be able to transfer to it if you have created a new one for your wallet.