Learn Italian: Noi siamo americani.

No, it is optional! Because the verb siamo can only mean "we are", Italians often drop the subject pronoun. You could just say Siamo americani. Including noi adds a little emphasis, like pointing out that we are the Americans.

Why does americani end in -i?

Adjectives in Italian have to match the number of people they describe. Because noi (we) is plural, the singular word for American (americano) changes its ending to the masculine plural -i to become americani.

If a group of women is speaking, do they still say americani?

No. If the group is entirely female, they would use the feminine plural ending -e and say Noi siamo americane. You use the masculine -i ending for a group of all men, or a mixed group of men and women.

Why is americani written with a lowercase "a"?

In English, we always capitalize nationalities like "American". But in Italian, words for nationalities are written with a lowercase letter when they are used as adjectives to describe someone.