What is the distinction between "du" and "ni"? Is one more formal than the other?
Du is singular and ni is plural. Ni can also be used as a more formal singular you, but it's not common these days.
I once read a book by a linguist, who did some research on European language usage. He discovers that the frequency of using the formal type of "you" (vous/Sie/Ni etc.) gradually increases when you go from north to south. So, basicly, Italians use it the most often.
Today in Italian we don't use the formal you "voi" anymore, it has been replaced with the third singular person "lei".
Oh Really? Surprise! Do you change the conjugation with it or just omit the voi and mentally assume it was lei?
Yes, we change also the conjugation. For example "tu sei", "voi siete", "lei è" (I used the verb "to be"). The history behind the usage of "voi" and "lei" in italian is very long and complicated and there are also regional differences, for example "voi" is still used in some regions of the South (for example in Naples). But "voi" was imposed by the Fascist government in the italian society, and later it was replaced by the feminine third person "lei" (it is feminine also if you are talking to a man... This is due to the origins of its usage...) :-D Insted the normal masculine third person is "lui", but only the feminine "lei" is used as the "formal you"
Will you explain further what you mean by "the origins of its usage"? Love to hear more