1) I assume you meant "Publisher" and not "agencies"?Most agencies sell authors copies of their books at greatly discounted price for signings and cons, etc. It's really not that unusual...
2) NO. Most do not. Signings in a book store, the store will order them in from the Publisher. Signings in other venues, typically a Store is commissioned to sell on site.
At book launches I've attended, the Author has had a local indie bookstore attend and sell the books beside her, as she signed and spoke with everyone.
My Publisher only put out, on average, 4 pic books, 2 other (either chapter, mg, ya... now THAT is small) a year and they still supplied the books to the booksellers for signings/conferences.
3) Conferences, same thing, though my experience in conferences is limited to Children's Publishing. At SCBWI conferences the bookstore consigned for the conference brings in the books for sale. Authors sign but can not sell.