I use two one gallons- and my bettas thrive, I don't think they could be happier as they currently are. And there isn't a whole lot of trouble heating a one gallon- you just have to make sure to get a heater that works best for your set up, and location of the tank.. and they require the exact same #/% water change per week as a 2.5- it all depends whether or not there is a filter.
Water changes every 2 days is too much- as the water can technically be too clean and could in turn put the betta at a disadvantage.
OP- I would only divide by one- as even though you are dividing into 1 gallons, it will be less then a gallon due to substrate and having the water level lowered to help prevent jumping over.
Having a male and female next to each other is no different then having two males, or two females next to one another. In time they will get used to each other, and they will flare/dance just the same regardless of sex. I have all of mine in rows and they are in perfect few of opposite sexes with no issues, no stresses and no ailments.
are great- I have some of the aquatic ones from PetCo.. cheap, easy to clean and heat. You don't need a filter for a betta as long as you are willing to do weekly 100% water changes.
The filter will depend on the size of the tank, and the flow of the filter- what size tanks it works best with.
For anything smaller then 5 gallons I don't even worry about a filter, as there won't be a stable cycle, and trying to vacuum something small can be frustrating.. I prefer to just do the 100%, but that is my preference.