Is it possible to lock all notes, and automatically lock new notes, on Notes app?
No, you can't set all notes to be locked. But that doesn't mean they're not all encrypted.

If you scroll ALL the way down in Passcode settings (if you have a passcode), you'll see a little line of text that says Data protection is enabled.

That means everything on your device is encrypted with your passcode. That's why Apple can't unlock it for you - it's silently encrypted.

Therefore, all your notes (if you have a passcode) are already encrypted. Adding a lock is an extra layer, but you can't add a lock automatically.

If you'd like notes to automatically lock, feel free to send apple some feedback at apple.com/feedback