when should I take out my old cycled media cartridge?

about once a month is fine. i actually never changed my current filter cartride for the past 5 years since i bought it i simply rinse it off in old tank water here and their and clean my tank every week no problems. i don't recommend this but this goes to show it can be used for a long time.

the reason why the oranda probably isn;t growing might be because your tank is too small. if your tank is too small for a fish that requires lots of room the fish will become stunted and eventually it's organs will explode and kill it. not sure if they actually explode but their organs do grow and continue and pretty much cause health problems causing the fish to die. do you also clean your tank once a week? what are the parameters of the water in the tank? the temp? these all contribute to fish growth as well as stress and food quality as well.

No, you don't need to. You should be rinsing the filter media with water changes though, just give it a swirl in the bucket of dirty water, not under the tap. The only time you should replace cartridges is if your tank is hit with a disease, if you need activated carbon to remove medication, color, or odor, or if it's literally falling apart. If your filtration is the problem then you actually need a stronger filter.

You could get a pre-filter sponge to stick on your filter intake, it will be useful for extra fine filtration, but it wouldn't be as good as getting stronger filtration. Also, orandas should be in a 30 gallon at the bare minimum. 50 gallons is ideal.

You can take out the media when its broken down and cannot be used anymore. I change my filter cartridge every 2 months because A local fish store says that could lead to diseases in my tank

Hope i helped :D