Capiche......slang, " Do you understand?" often used to imply a threat. The "e" on the end sounds phonetically like "eh". Sometimes it's dropped. Sometimes the "c" sounds more like a "g".
Capisci....more benign way to say it. You're right about the pronunciation, Equinox....or whatever your name is.
Comprendi......The form you'd most likely use if talking to the Pope or..........Al Capone. Much more formal and respectful. Of course the "i" sounds like "ee"
Take it on good faith from a son whose father was born in Priolo, Sicilia, in provincia di Siracusa.