PUR PLUS Faucet Mount Water Filtration System, Gray with 2 Mineral Core Filters

Does this come with any filters?

Has anyone had the filter just fall off the connector? It's happened several times when water pressure comes thru. It's installed correctly.

is there any filtering Difference between the horizontal and vertical styles?

Do the instructions say to turn the filter off when turning the hot water on or the filter would get ruined quickly with hot water?