Can I test an AFCI breaker hooked up to a 3 prong plug in a regular receptacle with neutral and ground connected to the pigtale or does it has to be installed in a panel box necessarily?
I can't quite follow your question.
An AFCI breaker has to be installed in a panel.
You can buy a receptacle tester that has an AF button on it to test this function.
You cannot connect the ground and neutral to a common pigtail.