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).
Maybe … multi-session screen sharing — the license for Mac OS X (Lion) uses the expression separate graphical desktop session.
Items of interest but nothing overtly related to screen sharing.
Open source
Released for 10.7 but some of what's there (example: Open Directory) is not amongst Apple's list of open source projects, so I would not treat the latter as comprehensive.
Again I can't see anything specific to screen sharing in Lion.
Timeline of recent documents in the Mac OS X Developer Library
http://developer.apple.com/library/mac/navigation/
Filtering the list of documents for the word screen doesn't reveal anything obviously relevant, but you might like to review that list occasionally.
Overall
Considering what's in the license, my hunch is that Apple will not be especially open about recent and forthcoming changes (if any) to screen sharing in Lion.
Update
Comments from bmike rung a bell. Apple's article HT4715 About Apple Remote Desktop v3.5 includes a section Lion screen sharing with the following information:
A third party VNC viewer will always be connected to the login window. If the login window is not on the display, a new login window is started that is not shown on the display. The screen sharing user can then log in with any valid account on that computer.
If a third party VNC viewer has difficulty, then maybe it's not following best practice, or the most appropriate standard … whatever those practices/standards may be! With apologies for teaching grandmothers to suck eggs (bmike won't need this but someone else might): http://en.wikipedia.org/wiki/Virtual_Network_Computing
Best Answer
A couple of options come to mind. You can try both and see which works best for you.
1) you can install VNC for Windows (there are several versions) on her machine
Most are free and should work with the OSX vnc client application. I haven't use it so I can't say more. As long as they on the same network you should not have any problems. Over the internet, things get complicated...
2) install a free (for personal use) application like TeamViewer.
I prefer Teamviewer as it is simpler and it will work from anywhere in the world with a semi decent connection. There are several other applications like this out there but I've used it for years and I've come to trust it.
The other good thing about TeamViewer is that once her machine has it installed (and password protect it), it will get an numeric ID that should not change. Open an account with TeamViewer.com and save her ID there. Then anywhere in the world you can find her machine and share her screen. Neat no?
Hope that helped.