How can I recover a blockchain.info wallet without the wallet identifier or the mnemonic?
Quick primer:


The identifier is a dash separated lowercase bit of text, like a32d0de4-818b-4aa3-...

It's specific to blockchain.info - other wallets use different systems. It was probably emailed to you.
The mnemonic is a 17 word bit of text, like skill course bleed oversize attempting lazer endure...
A bitcoin address looks like 175tWpb8K1S7NmH4Zx6rewF9WQrcZv245W. A bitcoin address is not specific to blockchain.info. It's how you tell the faucet where to send the money. This is not what you use to log in.
All of this is different from your email address or password.


Troubleshooting steps:

You need to get either the mnemonic or the identifier. The identifier was probably emailed to you by blockchain.info, so check there. If you get the mnemonic, you can recover the identifier on the login screen with the 'Recover Wallet' button. I think it's also possible to get the identifier by contacting blockchain.info support, but you need additional information.

Once you have the identifier and the password, you can log in.


  Also, I read through a few not so similar Questions and answers where they spoke of downloading the wallet, which I know for sure we DID NOT do. Is this something you have to do?


It's something you need to do for some wallets. Not blockchain.info, though.