How to address email to a professor who prefers informality?
If the professor explicitly says not to call him by his last name, then don't. It would actually be more impolite to ignore his request in order to conform to some abstract "formality" rules. 

However, even if you are addressing your professor by his first name, you can still preserve some degree of formality. Some common norms include: 


do not use slang
avoid excessive contractions (e.g. use have not instead of haven't)
use your full name in the signature
be polite


In general, the rule of thumb is to be respectful and professional in your communications. Sometimes that includes addressing the person as "Professor X" or "Dr. X", but it does not have to. Just make sure you sound polite!