Which part of a formal e-mail is optional?

the closing

the contact information

the person's last name

the salutation

Contact information will always be optional when you are writing to someone. It is an element of trust that is sometimes unneeded. Of course, if it is a business letter and they need to get in touch with you, that does change the purpose. But as this is a formal letter not a business letter, it is not an obligation to give an address.