Since the Screen Sharing feature seems to be the only one unable to connect, the best way to diagnose its behavior is by using the application directly.
Please, launch screen sharing located in:
/System/Library/CoreServices/ScreenSharing.app
The application has no visible "UI" so don't expect a fancy Cocoa interface. Instead, once you have loaded it, all you'll see is this "poor" icon in the Dock:
Click on it and then go to Preferences in the Mac menu bar. You should be presented with:
Notice the second option to only encrypt passwords and keystrokes. That's fine, but as you can see, there's no option to skip encryption altogether. Some VNC versions have incompatibilities with encryption, but this would be rather shocking since you're talking about OS X vs OS X.
In any case, once you have the settings like that, try connecting, again, in the menu bar: Connection -> New (or ⌘cmd + N).
A simple dialog appears asking you to enter the Host's name. Following your screenshots, try: 192.168.1.99 and hit enter.
We'll see what happens from here. Also, have the Console.app open on both computers, to see if there are any System messages going on (or anything related).
So apparently you can use the Back To My Mac infrastructure to get to SSH even if there's no port open on the router in front of the relevant Mac:
Find your iCloud account number by executing this command in terminal:
dns-sd -E
Example output
Looking for recommended registration domains:
Timestamp Recommended Registration domain
23:45:15.660 Added (More) local
23:45:15.660 Added icloud.com
- > btmm
- - > members
- - - > 123456789
(Make a note of the number on the last line, in this case 123456789 (this is just an example).
The hostname you need to use for ssh is <computer's local hostname>.<number above>.members.btmm.icloud.com. Replace spaces with hyphens, and omit apostrophes (the default name is "Name's <type of Mac>")
The command I used therefore was:
ssh -2 -6 Jons-mac-mini.123456789.members.btmm.icloud.com
To complete the solution to my problem (rebooting), once logged in via SSH, I used the following command to restart:
sudo /sbin/shutdown -r now
(Sourced from here)
Best Answer
There is nothing built into OS X that allows you to share your screen with multiple people at once.
One-to-One : Screen Sharing
OS X's built-in Screen Sharing is limited to a one-to-one connection. Screen Sharing is based on VNC and can be limited to observation only.
One-to-Many : Google Hangout / Skype
Consider using a Google Hangout to share your screen. While it does require third party software, the use of the Chrome browser is free. This approach also ensures no-one can control your shared screen.
Alternatively, Skype group calls allow for multiple people to observe your screen.