`ssh-add -l` displays that I have 3 RSA keys added to my SSH agent.

`ssh-add -L` displays those public keys.

How do I get the private keys as well, so that I can save them to a file? Or is it by design that this is impossible? How does it work then?

Can ssh-agent be asked to do operations using the private key? How can I ask it to encrypt/decrypt a number for me?

It's OK that I have to write code for this (the programming language doesn't matter), but I'd prefer using an existing tool or a library.