Maybe it's a colloquial thing, but to me, in the Midwest US, "laugh about me" just sounds completely wrong; no one here would ever say that. We always laugh AT people. You can laugh about an event, although even then, in most cases, it feels more natural for me to say I'm laughing AT the people or things involved in said event.
Idiom again. It's just part of the process.
If you compare the main Romance languages (Spanish, Italian, and French), you'll probably find more consistency in these grammatical constructs. It's English that's the odd duck, because English is a combination of Romance language (French mostly), German, Celtic, Latin, and Danish (Scandinavian), with some others thrown in there,
Ridete is second person plural - i.e. the speaker is talking to two or more people. The use of ridete (rather than ridi - second person singular) implies that all of those people are laughing (hence the 'all' in the translation). You should still be marked correct if you omitted 'all' from your answer.
While "of" is possibly the most direct translation of "di", prepositions rarely have a perfect word-for-word translation across languages, as they're often used in set phrases, and in this case, laughing "of" someone just doesn't work in English. You always laugh "at" people.
Laughing at people implies ridicule, no? When you laugh at someone it's because they've made a fool of themselves and you simply laugh at their misery.
"They're looking at me smilingly" might be rendered as "mi stanno guardando con sorrisi," though I'm not 100% sure of this.
The truncated form "why laugh at me?" carries as much significance in idiomatic usage as the version you quote as being correct. Incidentally, in the version at the top of this Comments page contains yet another version, viz: "why do you ALL laugh at me? Notice the difference? Get the act together DL.
It's what they do here to differentiate English's singular "you" from the plural "you". The Italian word "ridete" can be translated into English as "you laugh", but that loses the notion that it's a plural "you" in Italian. The "you all" is an attempt to bring that back into the English sentence. They say "y'all" in the southeastern U.S.