JAA/FAA pilot
You are mixing things up terribly. You have to follow the rules of the air of the foreign country. It has nothing to do with licensing. The problem you encountered is just because some authorities just don't know better, ie not used to dealing with FAA licenses. But flying US reg on an FAA ticket on the FAR's apply.
And you cannot fly on a JAA license in the States on US registered aircraft.
If VFR nightflying is allowed in a country, you CAN fly at night in a US registered aircraft as well. Some countries don't allow ICAO license holders to fly at night on the national register. As well as IFR when you have an IR.