Error code 100 is a problem loading the initial level cache, while 119 is copying files.
Try starting the game directly from the '..\SteamApps\common\Divinity - Original Sin\Shipping\EoCApp.exe' program file, by right clicking and running as administrator. Someone else had this combination of errors, and fixed by doing that. You can right click the executable, select Properties, switch to the Compatibility tab and check the option to always run as administrator (this should already be set for the GOG version of the game).
With an earlier version of one of the GOG installers for the Mac version, error code 100 could be caused by permission issues creating the initial ~/Documents folder. Getting the game to recreate the Documents folder would fix that.
The combination of rrror codes 119 and 120 (the latter a problem initializing the level cache) has been linked to problems with My Documents (a NAS becoming unavailable, or a replaced hard drive, but the Windows registry still listing the old path to My Documents).
Try creating a new profile, then start a new game and see if you can save and load. If that works, try copying your latest save folder from your current profile into the new profile and see if that will load.
Each save is a folder in the '..\Documents\Larian Studios\Divinity Original Sin\PlayerProfiles\<ProfileName>\Savegames' folder.
If a new profile and new game also give these errors, 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.
First disable Steam cloud support, if applicable, otherwise Steam would just sync to the online profile; this can be done 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).
After that, start D:OS, create a new profile and see if you can start a new game and save/load. If so, exit and copy a couple saves from the renamed folder into the newly created profile's savegames folder. If that lets you load the saves, move the rest of the saves over.
If that doesn't work either, delete the new My Documents D:OS folder and rename the original back again.
The next step would be to create a new Windows user account, leaving the My Documents folder in the default location, switch to that account, and then start the game directly from the '..\SteamApps\common\Divinity - Original Sin\Shipping\EoCApp.exe' program file, by right clicking and running as administrator.
There isn't a corresponding run as administrator function on Mac, but you can start the game directly from the executable: in the Steam library right click the game and select Properties, switch to the Local Files tab, click on the 'Browse Local Files...' button, exit the Steam client and launch the game from Finder.
If that lets you save and load properly, that would indicate the issue is with My Documents in the other user account (that was what prompted the person with the registry error to check there).
Are you shutting down all non-essential programs (especially anti-virus) before starting the game? Firewalls have also caused conflicts (though not with those specific errors, AFAIK).
For the Steam version, did you try verifying local files? In the library, right click on Divinity Original Sin and select Properties, switch to the Local Files tab and then click on the 'Verify Integrity of Game Cache...' button. This probably isn't an issue with the install itself, though.
