In a 5gal filtered tank...I would only recommend shrimp and/or snails...not big enough to properly house any other fish along with the Betta...
Water changes should be 50% weekly with substrate vacuum to maintain water quality
Filter media needs a swish/rinse in old tank water with a water change a couple of times a month and when the water flow slows to maintain good water flow and oxygen to the beneficial bacteria for the nitrogen cycle......
IMO/E-Changing the filter media is not needed until it is falling apart-unless you want to use carbon/charcoal and the filter media is the combo type-both the sponge and carbon together
If the charcoal is separate from the sponge-change the carbon per package direction-if combo type-either cut a piece of the sponge off the old one and leave in the filter for a week or so to seed the new filter media or make an extra 50% water only change a week for a couple of weeks unless you have water testing products to monitor ammonia and make water only change with ammonia 0.25ppm or greater....
Once the tank has matured (over 3months) usually you will have enough beneficial bacteria in the top layer of the substrate, walls in the tank and filter box, decoration, plants to prevent mini-cycles when the filter media is changed out....., however, it always a good idea to monitor the ammonia for a few days after large water changes and filter media change/cleaning and/or watch the fish behavior for changes and make a water only change as needed between the regular weekly water changes....
The fish and hobbyist are one of the best indicators of water quality and problems with the environment.......power of observation......
Charcoal use is a personal choice more than a need-weekly water changes do the same thing-remove odors, tannins, medication...etc......