Is it allowed to mount fake missiles on a civilian aircraft?
Importing former military aircraft


  Former military aircraft imported from ANY other country require an import permit issued by the Department of Treasury, Bureau of Alcohol, Tobacco, and Firearms (ATF). This is granted by ATF using an ATF Form 6, Application and Permit for Importation of Firearms, Ammunition and Implements of War. Additionally, these former military aircraft are required to be demilitarized in order to clear U.S. Customs (FAA).


Getting a certification


  Unless the aircraft are used for an approved civil research and development (R&amp;D) project, former military aircraft owners/operators must permanently demilitarize their aircraft before FAA certification (FAA).


So those aircraft are permanently demilitarized and cannot release ordnance or fire bullets. Since there are multiple examples, it is legal (in the US at least), and with the demilitarization there is no worry such aircraft would be able to release live ordnance if the owner somehow was able to obtain some.

Inert missile

I wasn't able to find text regarding mounting fake missiles, but a line from Dr. Strangelove came in handy:


  Air Force Base Guard
  You sure gotta hand it to those Commies -- Gee, those trucks sure look like the real thing, don't they? -- I wonder where they got 'em from? -- Probably bought them from the Army as war surplus...




I found inert ordnance for purchase, like the one above. And the blue line on the missile on the L-39 indicates it "does not contain a live rocket motor".

Livery

In AC 45-2E I did not find anything about using USAF or foreign military markings, but most probably that falls under freedom of speech in the US.



Related: Why can civilians not fly demilitarized US fighter jets?