First, your log doesn't show any errors, it seems as if you called GSX and then exited the sim yourself.
But the bigger problem is you have a VERY old version of the program ( build 4061 ), when the current version for FSX, and the only one we have online now, it's 4641 so, you are hundreds of versions outdated.
Since it's not possible to get such an old version by using our installers, it seems as if you either downgraded it, or you used a very old ( years old ) installer, and never updated it.
So, before doing anything else:
- Download and install the CURRENT GSX installer.
- Be sure your firewall is not blocking the download
- Add the whole Addon Manager folder to the antivirus EXCLUSION
- Run the FSDT Live Update again.
If that doesn't work, try the new Universal Installer and use that to update all products.
Another thing strange, is the line in your log saying:
"Current locale is C"
which should indicate the language of your Windows version, but it failed to print it correctly. Is your local Chinese perhaps ? That would explain why you couldn't get the updates, it's your country censoring the internet.