you need a heater unless the room the tank in is at the right temperature and is always steady.
as for a filter, ideally yes, less water changes and so on but betta are often uncomfortable with strong currents so need the filter to have a slower flow there are many ways of doing this most are putting something like a tight over the part where the water comes out as this slows the flow so male betta are better able to build their bubblenest and swim easier. i myself don't have a filter on my slightly smaller 4 gallon tank but the filter will help ith water conditions but is not essitanal you'll just have to do larger more frequent water changes compared to other fish.
also in some of the pinned topics under care for betta's etc. they have sections on filteration for more advice.
i'm using that idea of a sponge filter in under 5 minutes, making it tommorrow thanks alot for that.
hope that helps