What is context? I think most probably "корзинка" means "canister", "crib" http://www.sew-shop.com/images/product_images/popup_images/tilda/13318_0.jpg We do not use endearment form (suffix "k") for trash. Бросьте грибы в корзинку. Положи ягоды в корзинку. Or "корзинка" is a basket in the shop. http://autosliv.com/files/2012-03-25_kilmas_484.jpg Бросьте хлеб в корзинку. It is rather informal command.

If you want to use it as "throw that away in the trash." it should be written as "Выкинь это в мусорную корзину". Here is the difference between the "Брось" and "Выкинь". In this meaning "Брось" looks like "положи" or "помести", but "Выкинь" means "избавься".

It's just a command. We seldom use it as idiom. "Брось это в корзину для мусора"

I never heard it. Not once in my life (I live in the southwestern part of Russia) .What is especially weird in this sentence is that the diminutive "Корзинка" is used instead of the base form. "Корзинка" could mean something like a shopping basket or maybe a bast-basket, but never ever a dumpster or a wastebin ("мусорный бак", мусорная корзина"). I suppose this expression to be completely made up.

Слово "корзина" может иметь несколько значений. Корзина для мусора,корзина для товара в интернет магазинах,корзина -кольцо с сеткой в баскетболе.