That valve tube that they charged you I think is not just the cap but the whole thing that goes into the rim. Normally when changing rims/tires then they will check if the rubber seals of that valve tube still ok or not. If not then may leak, do they will suggest to change, but it's NOT always mandatory to change it every time you change tires/rims.

As for the plastic cap at the end, that's just extra protection from valve leaking, if not have also still can, and yes normally it's free unless those fancy colorful ones that you buy in accessories shops.