Learn Italian: Siete innamorati, ma non vi vedete mai. - You are in love, but you never see each other.

Here, vi acts as a reciprocal pronoun. While you have learned that reflexive pronouns show an action done to oneself, in the plural forms like voi (you all), they can also mean doing an action to 'each other'. So vi vedete means 'you see each other'.

Could vi vedete also mean 'you see yourselves'?

Yes! In Italian, the plural reflexive (yourselves) and reciprocal (each other) pronouns are exactly the same. Context usually makes it obvious. Being in love usually means wanting to see the other person, not yourselves in a mirror!

Why are there two negative words (non and mai) used for 'never'?

Italian requires a double negative when words like mai (never) come after the verb. You must put non before the verb and mai after it, creating non vi vedete mai (literally 'you do not see each other never').

Why does innamorati end in -i? What if I am talking to two women?

Innamorati (in love) acts as an adjective here, so it must agree with the people you are talking to. The -i ending means you are addressing a group of men, or a mixed group of men and women. If you were talking to a group of only women, you would use the feminine plural: Siete innamorate.