only the Ferrovie Laziali (FL Lines) as these are operated by Trenitalia (covered Railcompany)

Basically trains run by Trenitalia and Trenord are included. Also see the page about Italy:

https://www.interrail.eu/en/plan-your-trip/tips-and-tricks/trains-europe/trains-country/trains-italy

That means for Naples that only Metropolitana Napoli line 2 is included. The other lines are not operated by Trenitalia.

No, you can't, the public transport (bus and subways) of Rome is a separated company (ATAC, in Romans we call it "de merda").

Anyway, there are some regional trains of Trenitalia passing through some important stations like Roma San Pietro, Roma Ostiense, Roma Trastevere, Roma Termini, Roma Tiburtina, Roma Tuscolana. It is not easy to get around using only these stations, it needs a lot of walking, but it is possible Anyway the subway ticket of Rome is 1.5 euro, pretty cheap compared to other European cities.