I re-downloaded/installed gsx_fsx_setup.exe v2.5.0.6
Since the only version we have online now it's 2.5.0.8, this further confirm something is very wrong with your system, unless you downloaded it last week and are installing it now.
Just to add more confusion to the problem. I've never been able to get Couatl_Updater.exe to work. Even on new down loads I get the "Can't connect to the internet ....." warning. I have to always us Couatl_Updater2.exe to get Live Update to work.
You have one and only problem: which is some software, either a firewall or antivirus, which is blocking the download of files. This cause BOTH the updater to fail AND the message about "out-dated" files.
Some users have more than a firewall or more than an antivirus running together, without even realizing it. I witnessed this first-hand when helping someone in remote assistance, someone who was also "sure" he turned off firewall and antivirus.
So, please, check *every* software you installed that might affect your internet connection, like an anti-spyware, and internet security, a VPN or anything that sounds remotely similar because, BOTH your issues are clearly caused by something which is disrupting the normal download of files.
Restarting the modem might help as well, to get a new IP.