You can use the ".zip" version which should give no issues with the anti-virus. We are using NSIS (nullsoft installer) to create our self extracting installer. I am thinking, it is most likely a false positive, which evidently, NSIS is known for. See https://nsis.sourceforge.io/NSIS_False_Positives
I can reproduce the issue here (I am also using AVAST), and the installer exe is blocked when I try to run. I have reported it as a false positive. Though I don't how long it takes for it get added to the virus definitions.
For fbc.exe switching to full screen problem, maybe try the mingw-org build of the compiler, not sure about that one. I can't remember last time I ran console in fullscreen on windows, so maybe worth some investigation on all versions. Thanks.