Bettas do best in slack water, for sure, they don't like currents. You would probably be best off with shrimp, but they again aren't really keen on big currents. The thing with such a small tank is that the volcano has more of an effect in a small tank than it would in a larger tank.
I have 2 types of media in my filters - sponge and ceramic. The sponge carries out the mechanical filtration, ie taking gunk out of the water. The ceramic provides a good home for the bacteria which remove ammonia and nitrite from the water. I do not use carbon.
Carbon is used for the removal of heavy metal pollutants (eg copper). Once it has been in the water for a few weeks, it loses its ability to perform that task, whether or not it has actually done so. This is why the manufacturers tell you to change it every 4 weeks. However, since my dechlorinator (and indeed, all the decent dechlorinators I have ever come across) also removes heavy metals, Therefore, I do not use a carbon filter, and thus save myself countless £££ per year. Never change ceramic filter material. Only change sponges when the old sponge is literally shredded to pieces, and even then don't change more than a quarter of it.
With regard to water changes, I would recommend you do a 50% water change weekly, since in a 5 gallon tank, issues can build up very quickly.