It could stop your medication or slow it down a lot, yes. The meds would be filtered out of the water by the carbon.
Depends on your filter. You can buy black sponge pads with carbon on them for most filters, and also you can buy bags of carbon (basically charcoal I think) that you put into bigger filters. Not sure on price, but for something like a Fluval 3+ you're maybe talking £3 or £4 for 2 pads maybe? Not vastly expensive but over time it builds up.