Telegram – Are Messages Delivered After Deleting a Chat?

if the messages have been delivered, then telegram deletes them only if the recipients have deleted them as well

When you delete a message, you delete it from your message history. This means that a copy still stays on the server as part of your partner‘s message history. As soon as your partner deletes it too, it’s gone forever.

Sadly, there's no way to backup secret chats specifically. The rest, as you know, can be backed up and exported. But secret chats are bound to the device so they'll be gone once you reinstall the app. Even screenshots might not work as they come out blank in some cases (to keep the secret chat, well, secret.) It's a sacrifice for the sake of extra security.