Is screen sharing under Sierra secure, i.e., a fully encrypted connection?
Solution 1:
The answer depends on how you connect to it.
If you're using a standard VNC client to connect with a password only, nothing is encrypted. Not even the password.
If you're using the Screen Sharing app on macOS 10.8 (Mountain Lion) or later to connect with a username/password or AppleID, everything is encrypted.
If you're using the Screen Sharing app on macOS 10.7 (Lion) or earlier to connect with a username/password, the exchange of credentials as well as keypresses and mouse moves are encrypted by default. However the actual screen display (i.e. the graphical content) is not. You can enable full encryption from the Preferences menu in the Screen Sharing app.
If you're using VNC, I would recommend wrapping it in encryption using for example an SSH tunnel, encrypted VPN or similar measures.