Re: Battlelog-web-plugins_2.1.3.109.exe will not "run" or "save"
Sounds like your AntiVirus program is a bit over-zealous. Try disabling it just while you install the plugin.
Only download it from the source not from any direct links players have been posting around the forums.
Check that Origin & Battlefield are added to your AntiVirus Exceptions List.
Alternatively you could try easing the restrictions of the AV a notch, or consider using a different one like Microsoft Security Essentials, AVG Free, MBAM AntiMalwareBytes, BitDefender.