If you mean a literal “&”, none of the proposed forms is meaningful. In an informal communication, you'd use the first name followed, if necessary, by e famiglia. For instance:
(Saluti da) Mario e famiglia.
In a formal context, you might use famiglia followed by the family name:
(Sentite condoglianze), famiglia Rossi.
It's pretty unusual and impolite, and also shows an ignorance of at least one of the functions of language.
As for which way to close a conversations, friends or close colleagues will use a normal Ciao (there is a recent custom of closing a phone call with a sequence of generally three ciaos). People who are in less intimate relation would say Arrivederci (...
It is not normal to sbattere/chiudere/riattaccare il telefono in faccia (hanging up a phone call) nor andarsene alla chetichella/all'inglese (slipping away quietly without saying goodbye).
I personally find strange many TV series where they never say goodbye at the phone, and most of them are American.
Although I must say that in some circumstances it could ...
You use ciao in an informal situation, with your friends and with someone you know.
You use buongiorno in formal situations , when you first meet someone. It is considered a polite and respectful greet, used especially with older people.
Obviously this form can be used instead of ciao but never do the opposite or you could be considered rude.
According to this page a formal salutation could be
Reverendo Padre Rossi
is slightly less formal.
Also according to the same page, the letter should end with a phrase like
La prego di accogliere, Reverendo Canonico (NAME AND SURNAME) l'espressione dei miei sentimenti deferenti
(YOUR NAME AND SURNAME)
Usually is typical for an Italian person to say goodbye with "ciao" or "ci sentiamo (dopo, domani,...)" at the end of a phone call or with "arrivederci" or "ci vediamo" when leaving the house; it also depends whether it is a formal situation or not.
Obviously it is impolite to hang-up without saying goodbye or some kind of salutation, but that's true no ...
You can find on Treccani's appellativi e epiteti [prontuario] a list of proper forms for most of ecclesiastics and their abbravistions.
For a bishop:
(Sua) Eccellenza (S. Ecc. o Sua Ecc.): vescovo o alto prelato; nella
tradizione, prefetti e questori, e così via;
for a cardinal:
(Sua) Eminenza (S.E. o S. Em.), Eminentissimo (Em.mo, E.mo):