Assuming you have access to another person's device, set up a SOCKS5 proxy, install a root certificate to parse the SSL traffic, and take a screenshot of the private key of a private chat.
Is it now possible to use the proxy to record a message and manually decrypt it with the private key?
Is this the private key used to encrypt and decrypt the messages? On Telegram FAQ, you can read "this is not the key itself, of course!"
If not, is it possible to derive the encryption key from it? Or is the private key only stored deep in the app?