How do you typically refer to a fellow Italian in different settings (formal, informal or the homestead)?

There are few precise rules, in Italian, to address directly another person by name, and surely not so varied like your examples.

Take a person named Domenico Rossi; the most informal way is to call him "Signor Domenico Rossi" (very very formal) or "Signor Rossi" (more common, less formal); these forms are used by people when there is not a continuous relationship or when that relationship is formal. This addressing is combined with the courtesy form "Lei". In brief, it is common to use the surname alone unless the context is very formal, or if there is the possibility that there are two persons with the same surname that can be involved.

In case of colleagues or not so intimate friends, the "Lei" form is dropped, and simply the name is used: "Ciao Domenico". In this case, and in very particular situations, the name can be modified using a diminutive, for example "Ciao Domenichino" ("little Domenico"), showing some form of affect or empathy, or attention.

Coming to intimate friends or related, sometimes a different/modified name can be used, and that modified name is always used. For example, Domenico can become Meco, Checco, Nico, Mimì, but the addressee must "accept" (or must be used to) that modified name. I mean, if Domenico is called Meco by its related, his friends can call him Meco, probably because he presented himself this way to them, and for them he is always Meco, even knowing that his real name is not Meco.

These modified names do not follow strict rules, and many names (for example Mario) are rarely modified. Some names, especially composed ones like "Gianpaolo" can be shortened in "Gian"; or "Federica" (which is not composed) can turn to "Fede". Some example are:

Sabrina: Sabri or Sabry, Brin
Federica: Fede, Chicca
Concetto: Tino
Valeria: Vale
Nicoletta, Concetta: Cetta
Luigi: Gigi
Giuseppe: Peppe, Beppe
Antonio: Toni or Tony

In these shortenings, the dialectal influences bring many forms, sometimes funnier; for example for piedmontese, Bartolomeo -> Tromlin, Giuseppe -> Pin; or in the south Barbara -> Varve, Bartolomeo -> Martemè, Corrado -> Cherrare. And there are many many other.

I've found two listings of regional/dialectal abbreviations:

http://www.carusa.it/SPIGOLATURE/Diminutivi_e_nomi%20rari/diminutivi/index.htm

https://it.wikibooks.org/wiki/Lombardo/Nomi_propri_di_persona (look in "diminutivi")