As far as I do understand, you want to convert an authentication subkey to an SSH key, and authenticate using this.
If I generate a PGP subkey that only has the authentication capablity and use this to generate an SSH keypair to authenticate Git for example, does this pose a security threat?
Whether this is reasonable or not depends on what you're trying to achieve. The important parts of OpenPGP are its key and trust management features. When you want to use those for authenticating using SSH (monkeysphere makes this possible, but requires some configuration), you completely hand off key management from SSH to OpenPGP, making adding, exchanging and revoking keys much easier. If so; go for authentication subkeys, they offer a real advantage!
If you don't want to use those extended capabilities (or just might use them at any time in future without specific plans), don't do so. You're adding up complexity (which is always a bad thing in information security) without actually having an advantage. For example, you won't be able to use the extended capabilities of monkeysphere with GitHub -- so better directly stick with a good old normal SSH key, you'll have to "revoke" it manually anyway (but removing it from the GitHub account panel).
Generally, reusing secrets will result in more systems/services falling for a single breach in one of them, so generally doing so is a bad idea; but the advantages in key management might be worth the slightly larger risk. If you're not using OpenPGP authentication keys otherwise anyway, there is no further risk in an authentication-only subkey being used for SSH, because there's no other service it could be used for.
When I do, should I use my PGP private key, or the public authentification subkey?
You would have to store your public authentication subkey on the system on which you want to be able to authenticate. Your private key stays private and is used to answer a challenge sent by the authenticating server.
Then when I add my passphrase-proteced private SSH key (./ssh/id_rsa) using te ssh-add command, I am prompted for my passphrase. But then when I make subsequent commits using Git, I am not prompted for my passphase by the SSH Agent. Why is this?
Authenticating using SSH and signing using GnuPG don't have anything in common. I don't quite get your question; you might want to be more specific on what's requesting your password (and where you'd expect it) and how you add the OpenPGP key to the ssh-agent.