the heater may not be working because it's not in enough water. i know all the heaters i've had have a line on them and the water level is not supposed to go below it. if your tank is only half full that may be why. what brand/kind is it?
as for the bulbs, i've heard from a lot of other members that they rarely grow so i'm thinking yours not growing is nothing new :(. if you want live plants you'll have to get some that are already growing. otherwise silk plants are a LOT easier to keep, lol.
as for breeding your bettas i'm not an expert, i've looked into it but it's really a lot of work to raise the fry and you could potentially end up with a ton of little baby bettas. you'd have to find homes for all of them have houseing for them while you find a buyer, etc. make sure you research as much as you can before breeding!
best of luck!
"Just don't tell 'em I've gone crazy, that I'm still strung out over you..."