In Italian, there are two choices for love, which you use depending on who you talk to. "Amare" is romantic love, so "Ti amo" (I love you) should only be used on, say, my own husband. If you are talking about loving your parents or children, then it's "Ti voglio bene" which literally seems to mean "I want good" but I think it means "I want good things for you". Anyway, both those phrases translate into "I love you" in English but you have to know which is which.
The other Italian ones you listed are not as varied as you think:
amare: to love (verb)
adorare: I think this is really "to adore" which isn't quite the same
amore: love (noun)
amante: one who loves, lover
affetto: affection, sort of platonic, a friend may write "tanto affeto" (=much affection) in a letter
amoroso: full of love, amorous(?) (adjective)
amorosamente: full of love (adverb)
So you see they don't really cover much more territory than the English ones. For me the biggest distinction is the Ti Amo/Ti Voglio Bene split, which I find English doesn't sufficiently separate.
