Hi again, Ange... that's not a dumb question at all. You're just a beginner at this, so you're not supposed to know all the answers yet. We all learn best through experience anyway and need to weigh carefully the advice we get from all different sources. That takes some time, as well.
Your instincts are dead right about the heater... and also about not wasting your breath to argue this point with some guy at a pet store. Keeping fish at the wrong temp for their species plays havoc with their metabolism. This can lead to illness, infection, other pathogens, and severely shorter lifespans.
The sponge filter should be easy and inexpensive to find locally. And if all else fails, you could post a "want to buy" ad here in our classifieds forum. Lots of our members have used equipment they can sell or trade and who know a lot about small tank setups. Adding some filtration to the tank will help keep your parameters stable and to avoid poor water quality issues. As you can, you should also invest in a reliable liquid test kit (such as API) to monitor your water parameters on your own.
As you read up more on fishkeeping, you'll soon find out that smaller tanks are much more difficult to maintain than large tanks. This is because they have seriously wide swings (which will unduely stress a fish)... irregularity in temperature... just about anything you might want to measure is going to vary a lot and be unstable. Also, just because the water looks sparkling clean this does not mean the water quality is adequate for the health and well being of your fish.
Without a heater and proper filtration, you might as well be keeping this betta in a 2.5 gallon bowl. And... while you will find many people who debate this point by saying it's okay to keep a betta in a small bowl, those same people will usually tell you they've had great success with their betta this way for the last 2-3 years.. or so. The fact remains... a betta's potential lifespan if kept under proper conditions is 6-7 years. Some have even been known to reach 8-10 years of age. This is something you won't see happen with a betta that lives in a bowl or small tank without a heater/filtration.
Keep us updated with new photos and info about your setup and your lovely fish. Have fun and enjoy the hobby... and, by all means, keep asking all the questions you might have. Doesn't matter at all whether they're dumb ones or not.
Best of luck!
