Great question—Thanks for asking! Yes, make your key offline for security, and no, you don’t need to be online to do it. I differentiate between the key and the seed phrase.

You make your 128 (or 256) bit private key manually and completely offline. You will need to touch a computer to #bitcoin (make receive addresses, sign transactions), and at that point you can make a checksum. Why do you need a checksum? Primarily to prevent mistyping the key’s seed phrase, and it’s an input for HD wallets. As you are already entering your key into a computer by that point, checksum is just part of the process.

The good news is you can do all of this offline by severing the internet from your calculations—there are a number of tools for this.

TL;DR is anything you do beyond key generation requires a computer