1) What file extension should I save the private key from cPanel using? .pem? .txt? Does this even matter?

There's no standard extension for PEM keys. And indeed, it does not matter.

2) When I try to import my cPanel private key into PuTTYgen, why does it say, "Enter a passphrase for key"?

I do not know cPanel.
But according to this page:
https://web.archive.org/web/20200919160337/https://www.eukhost.com/kb/how-to-manage-ssh-keys-in-cpanel/
... There's "passphrase" field on the cPanel SSH Key Generator page.
(maybe the field got unintentionally autofilled by your web browser)

I generated a public/private key pair using PuTTYgen, and that works great. This allows me to establish an SFTP connection using WinSCP.

Out of curiosity, I also tried getting the private key generated in cPanel at my hosting provider to work with WinSCP. I realize that cPanel does not create SSH keys in the .ppk format that WinSCP wants, so they must be converted using PuTTYgen.

Two questions:

1) What file extension should I save the private key from cPanel using? .pem? .txt? Does this even matter?

2) When I try to import my cPanel private key into PuTTYgen, why does it say, "Enter a passphrase for key"?

Whatever I enter here, including leaving the "passphrase" field blank, is rejected when I try to import my private key from cPanel!