When I tried to create a private key I found that I was being asked for a password. I don't remember ever setting a password for the wallet
When you select the "Export private key" option from MultiBit Classic... it "prompts" for 2 different passwords.
One is the "wallet" password. If your wallet listed on the left hand side of the MBC window doesn't have a little padlock, it ISN'T password protected, you can leave the box empty.
The other is the "encryption" password to use for the export file. You need to leave this empty, otherwise the export file will be encrypted and you won't be able to open it up and read your private keys.