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Your instructions say to hand over my keys as a memo..

No you don't need my private keys, you just need my @name

yes.... When sending from bittrex to a steemit account you can leave the memo blank. When sending from a steemit account to bittrex you need to use your personal bittrex memo.

If anyone sent their private keys via memo the first person to use them to log in and change they keys would have full control of that account and it's steem