Well is a succinct English equivalent of 'bene'. In a good way is a less abbreviated English equivalent. Either way, the word functions as an adverb in a Latin sentence.
bene is bono, buena, good!
Abbastanza bene in Italian means "quite well" in English.
You don't. Mangia bene is Italian. In English you say "eat well."
bene factum
Stai bene con i baffi? in Italian is "You're fine with mustaches?" in English.
va bene?
"Hope you slept well!" in English is Spero che tu abbia dormito bene! in Italian.
"Okay!" in English means Va bene! in Italian.
"I am well" in English means Sto bene in Italian.
"Good! How are you?" in English is Bene! Come stai? in Italian.
Bene, grazie
Va bene
sto bene