is buying second-book beneficial to the author?

answers1: No, not in the least. In the same way a second-hand iPod
won't see any profits sent Apple's way, an author won't see any kind
of money from the sale of their book second-hand. They get a cut from
the initial sale (i.e. perhaps $1 from the sale of a $20 book) and
that's it. If you want to support your favourite author, you should
buy their books new.