As I said before, the aquaclear will help on the side it is in. The divider (mesh) will block the surface flow on the other side, so the other side will develop a slight ammount of a protien film. You can keep this to a minimum if your tank is clean, cycled, and has a top on it.
You should read up on the nitrogen cycle
, that link is very good. Cycling your tank reduces the ammount of water you have to change, and increases the ammount of fishies/bioload your tank can handle.
Basically, the aquaclear is a filter that helps with cycles.... You'll want to establish one so you don't have to do 100% water changes. THey're a pain in anything 5 gallons or larger. Since you only have one betta boy right now, cycling fish in should be reeaaallly easy and extremely safe. Just keep the filter running 24/7, and do a 50% water change once a week. Since you have only one boy, and you'll probably do it fish in style, it'll be a slow cycle, but eventually it will in fact cycle. When it does, you'd just continue doing the 50% water changes, so nothing really changes.
Carbon filters aren't necessary if you set up a cycled tank, you just need filter media (like filter sponges) to provide surface area for the good bacteria which convert ammonia (dangerous) to nitrite (dangerous) to nitrate (not so dangerous).
Personally, I'd stick with a divided tank for two boys if I were you. Sororities do best with 20 gallons or more. Seeing as you need at least 6 girls to spread out agression, they tend to look a bit cramped in a 10 gallon, and having so little gallons per girl means illness can actually spread easier.
I know you said you didn't want to divide the tank until your boy dies, but I hope you know most bettas live about 5-7 years.... It'd be perfectly fine to divide the tank that Honeycomb is in if you want another betta. There might be a bit of flaring to start off, but that's common whenever you divide tanks between two boys.