When you use "cheat on smb", it implies conjugal infidelity.
eg Jane left her husbund after she discovered that he was cheating on her.
"In" is used after "believe" when you mean a kind of religion (to believe in God, in miracles, in signs, etc) or some principles that one may follow in life.
eg Do you believe that the number 13 means bad luck? No, I don't believe in superstitions.
eg My mother believes in herbal medicine.
Compare:
Henry doesn't believe that such a thing as love at first sight exists in nature. (He thinks it is a myth.)
Henry doesn't believe in love at first sight. (He doesn't believe that such love is firm and lasting, but he doesn't doubt that such love exists, though.)