Yes, you want to remove the carbon from your filter so that the meds will be more effective . The other media can stay.
It's a good idea to have a few plants or rocks/cave in the QT tank to reduce stress on the fish. They'll feel more comfortable if they have hiding places.
As far as your stocking, I think you are near your limit given that your guppies will be increasing your population. Most fry will get eaten but some will survive. The cories and tetras are schooling fish and should be kept in groups of at least 6 but you would need a larger tank if you were to increase those groups.
Sorry Money, I don't agree that you can stuff 40 fish in a 16 gallon tank just because you have good filtration and do lots of water changes.
Granted, these fish are all smaller and will stay around 2" but I think overcrowding them would cause more health problems.