When the first problem occurs, are your stats also reset to 5? This is a known issue, and reloading is the only solution. A couple people have noted that if the host switched to doing something else while waiting for the other player to join, or the other person took awhile, it seemed like this was more likely to happen. One person reported they tried sending a save to the other person to host, and the problem still occurred, but when they switched back it stopped. Based on that someone else said they transferred a save to the person joining and without doing anything else the problem stopped. However, the game doesn't actually do anything with the saves when joining another game, so that appears to just be a coincidence.
For the crash on exit, does it happen if you just start the game and exit on the main menu? What if you start or load a single player game?
Was it your main system drive that crashed, or just one you used for games?
If you had to re-install Windows, make sure you update all drivers, etc,
Try re-installing the support packages for the game from the '..\SteamApps\common\Divinity - Original Sin\_CommonRedist' folder.
Are you shutting down all non-essential programs (especially anti-virus) before starting the game? Firewalls have also caused conflicts.
If applicable, disable cloud support either globally (in the client click on the Steam menu and select Settings, and then Cloud) or just for this game (in the library right click Divinity: Original Sin and select Properties, then switch to the Updates tab and check the Steam Cloud section).
Next, try browsing to the '..\Documents\Larian Studios' folder and renaming the 'Divinity Original Sin' subfolder.
This folder contains the saved games, configuration files and a level cache folder. Deleting or renaming it will get the game to recreate it on startup; playing the game from a different Windows user account would effectively do the same thing.
After that, start D:OS, create a new profile and see if you can start a new game and exit without crashing.
If that doesn't help, you could delete the new My Documents folder and rename the original back. If you don't have any saves, though, the only thing to restore would be any custom settings.
