1. It's not a true past tense; it's referring to a hypothetical or supposed situation, similar to "What would you do if you were rich?".
2. "his" = "Love's", "he" = Love, "him" = Reason, "his" = "Love's".
The way I read it, it is saying that people use (or try to use) reason to "cure" themselves of love, but not to advise them in matters of love.