When I tried updating MacKeeper through MacKeeper itself, I received report of a network error. Should I update it directly through the site and if so, how?
In order to update the product, you need to be connected to a stable Internet connection. This might be the reason why you got that report. To update the application through the official website, you need to access it and download the latest version. After you did this, simply run the installer of the new version. This should replace the old version.