Arachidi and noccioline is the same thing. Arachidi is the more formal name of “noccioline” but both mean peanuts (botanical Latin name: Arachis Hypogaea). Arachidi obviously are a direct derivation of the Latin botanical name “Arachis”. Italians will understand either denomination.
You have not mentioned Hazelnuts, which are very popular in Italy and grow wild everywhere. They are used in many desserts like Nutella spread, gianduia, gianduiotti, hazelnut chocolate, gelato. The Italian word for hazelnut is NOCCIOLA (plural: NOCCIOLE).
I doubt you will need to worry about Macademia in Italy. I’ve never seen it there.
Under your last post, under Frutti di mare (seafood), I don’t understand what you mean by “pescare” and “crostaco”. The former is a verb which means “To Fish”, the latter is not correct. Crustaceans in Italian is spelled CROSTACEI, which is the generic names of all crustaceans, aka anthropods,
Frutti di mare is a generic term for seafood (other than fish), it includes crustaceans like shrimp or scampi, but also shellfish like clams or mussels. The most common seafood in Italy are VONGOLE (clams), COZZE (mussels), GAMBERI or GAMBERETTI (shrimp/crayfish), SCAMPI (prawns), ASTICE (European Lobster), ARAGOSTA (Lobster), GRANCHIO (crab).
CAPESANTE or PETTINI DI MARE (sea scallops) are not as popular in Italy as they are in the US, which is great for me since my wife is badly allergic to those.