The bacteria will grow on anything in the tank but most is in the filter.
Some filters like marineland penguins have a biowheel that never gets replaced and the aquaclear filters have seperate components that can be removed. Unless you are totally scrubbing your tank and all things in it, you should always have BB growing it it assuming it is cycled. Weather removing the cartridge will crash the cycle - I don't know- I have always been told that it will and that is why you should never throw out the cartridge. It may depend on the amount of stuff you hav inside the tank as well.? Live plants also play a part - if you have any.
Carbon lasts about a month but IMO, its not needed. If the water smells, then you have a problem someplace - maybe a broken heater or you need to do more water changes. In my tanks, what I do is skip the cartridge completly and stuff it with aquaclear foam. It will last alot longer then the cartridge - just swish it in old tank water every so often. I have aqueon quietflow and tetra internal filters. I also stick some foam at the outflow to baffle it a bite more