If you have activated your 2FA on your account then it will usually ask you whenever you login. But in your situation, if ever you can login on another device despite having the 2FA activated, that's really odd.
If I am asked for an Authenticator code to withdraw funds it will fail. I wonder if there is any other way to test this without actually trying to withdraw funds.
You have deleted the app or the one that's showing your 2FA code on the app? it's unclear to me sorry. But this is the purpose why 2FA is important, you'll not be able to take it out if you don't have it. In this case, you need to contact the Coinbase support and explain this problem you have.