Can I recover REP if I sent it to my account that was created in the Augur beta app?
Augur generates an Ethereum public/private keypair for you, however we happen to be currently running the beta on a private test network. This means if you send real ETH or REP to your Augur created account, you won't see it within the Augur UI.
You can easily recover REP or ETH sent to your Augur beta account. You must go to your "Account" page, where at the bottom there will be a button for "Download Keystore File". This is an encrypted JSON account file of the Ethereum account you accidentally sent your REP/ETH to.
Head over to MyEtherWallet with that JSON file, and go to "Send Tokens". Upload your JSON file, decrypt it with the password you used when signing up on Augur, then you will see your ETH/REP on the main Ethereum network. You can send it out of that address and into any other address you control. (Keep in mind: you'll need a bit of ETH if you want to just send REP to pay for gas costs).