Why is cert.pem not being auto generated?

You do get the basic gist of the 3 options.

Yes, certbot will recreate it for you.

It wouldn't really; but in that recreation process the matching cert will also be created. And hopefully clear up the problem.

As for the snakeoil option, that is just to get it to "work" enough so that you can get a new cert (which should replace the snakeoil cert)