Assuming that you are talking about the "Master Key" in here, then unfortunately there isn't any way to retrieve that key for an account created via SteemConnect. It is both the beauty (for security purposes) and the disadvantages (can't recover lost/forgotten accounts) on creating accounts on a Blockchain. It gets worse since usernames can't be edited out or deleted so one have to settle for another user handle.
However don't lose hope yet, if you are not using incognito and have not cleared your cache yet then you can check if the key was saved on your web browser. One way to do this is to go to
Settings > Advanced Settings > Managed Passwords
No. There is no way of retrieving the key. When you first get the account you are warned that once it is gone, it is gone forever. You need to save your keys somewhere safe in case something happens.
There is no way to do that. Nothing is stored on their servers so if you don't save the keys yourself, they are gone for good with no way of retrieving them. There is no such thing as forgotten password recovery on the STEEM blockchain(or most blockchains) due to security issues.
You can't, I created a new account using Steemconnect and didn't copy the key at the right time and it cost me 10 Steem. I tried high and low to get support, even asking questions here but to no avail. Its a confusing and poor process and I know others have had the same issue.