The Rules really depend upon which country you wish to fly in. Whilst all ICAO countries will allow you to fly on an ICAO PPL, most countries have a validation proces, the FAA issue you a FAA Restricted Licence for example. The UK is about the only country in the World that allows you to fly witrhout a local validation. It all depends upon the Law in the country concerned.
Germany require a validation.
As to the rules regarding; can you then fly to another country, the 2 out of 3 is rather simplistic. Again it depends upon the Law of the countries concerned. The State of licence issue, the State of aircraft Registration and the State you wish to fly in. All 3 must permit it.
You can fly an N reg aircraft on a UK licence, the French do not not object to you flying it in France but FAR-AIM does not permit it, as the FAA authority to fly a US registered aircraft overseas only permits it in the country of licence issue.