In a real talk, you can say it without noi or (voi, loro), but in this lession you should try to use them.
Of course it has! singular: la donna and plural: le donne - for example: Noi siamo le donne (We are the women)
No. "Sei" = "You are". "Siamo" = "We are". See under the verb ESSERE. http://www.italian-verbs.com/italian-verbs/conjugation.php?verbo=essere