Payment Form: let the customer view his payment history.

Is there a way for me to add the option for a customer to enter their info (ie. name and birth date) and be navigated to view their account history?

Do you mean like preview users answer before submitting? If that is correct, you can add the Preview Before Submit widget: https://widgets.jotform.com/widget/preview_before_submit 

NO.. for example: A customer has been paying on their credit card bill for the past year. I want the customer to be able to log into my website and view their account history. Is that possible?

No, JotForm does not provide that type of service.