bettas are very hardy, there's a lot of controversy about bettas about if they can live happily in a bowl or not, if they should have a tank, blah blah blah, personally (and i'm typically not this blunt about things but i've had a sort of rough day and don't care if people get upset at my opinion) i think everyone should just get over themselves and trying to force thier opinions and beliefs on other people. I've had bettas live long healthy lives in bowls, and I've got a betta tank where i'm designing dividers that way i can keep multiple bettas in one tank. It's only a ten gallon and i'm sure there are people wanting to yell at me and say i'm over crowding it but like i said earlier, that's your POV and opinion.
The thing with bettas is that they aren't strong swimmers and they like slow-not moving water, which is why filters are hit and miss in my opinion (which is still just my opinion!) and why bowls are so popular. Bettas do need a steady temp of 76-79 for year round comfort and health and 80 to 82 as breeding temps.
As far as the feeding issue I would try freeze dried blood worms. Bettas LOVE blood worms, and if the freeze dried versions aren't working for ya then buy some frozen ones (cubes are very convenient), thaw out a small portion of them, like three or four individual worms, and try feeding him those. The best way i've found to do this is to get a small shallow bowl or something, fill it with water from the tank and hold onto one side of the cube and kinda wiggle it in the water. the cube will start to thaw out and once you have the desired amount of food thawed out then you can place the un-used portion back in the freezer. If you have other fish tanks then you can thaw some out for them as well.
Something else to think about is that maybe he is eating it but the bits that he's swallowing are so small that you aren't noticing them. Either way I'd say that the blood worms would be better for the betta overall. He is VERY pretty by the way. I have one like that but he ended up turning entirely that shade of purple which is really pretty.
Sorry for the tirade but I hope my info helped!
I don't think there is anything wron with 3 dividers in ur 10g! they still get 3..3g each! Really everything depends on the betta... Some will be happy and make nice bubble nests in bowls while others need a heater and space to move. I just figure its better safe than sorry so I get all my bettas cycled homes