AFAIK, modern decent AVs have no problems with CF so i really don't understand why i should "Disable Firewall, AV.." i have Avira running and it doesnt do anything to CF and the game works fine with it, not sure what you guys install.
As for the problem for some reason the launcher is stuck in a loop. Based on my experience with similar problems with the launcher you may consider this:
-Check the log if it says anything
-Replace the Freelancer.exe and cfwd.exe with the one from the FLMM Folder, so you have that launcher executable that is shipped with the initial CF installation (solved a lot of launcher problems in my cases)
-Restart PC and Router
-It is possible that the server cannot be reached when you attempted to play
-Did FLMM gave any errors when it was applying the mod?
-Make sure that .NET (4.0 or 4.5)is correctly installed (should be on most cases, but you any never know)