Not sure if this fall under Intellectual Property or not but seems the closest subject on the list. I want to know if it is legal to do an impersonation show where you are portraying a singer or dancer in the show

Impersonation of celebrities for commercial purposes falls under the celebrity's right of publicity. In general, any person has the right to prevent his/her image/likeness/voice from being  used by someone else for commercial purposes. However, publicity rights are different in every state and what may be permissible in one state may not be permissible in another. For example, the rights vary from state to state depending on whether the celebrity is living or deceased. You need to consult someone who knows the laws governing the right of publicity in the state(s) that you will be performing.