Larger tank with filter and heater needs to be "cycled" first. In plain words it means that you need to grow "good bacteria" that can transfer harmful fish waste, bacteria from un-eaten food etc. to less toxic nitrate. Frequent water changes, especially in the beginning are very important until the cycling is finished. Then 50% once a week should be adequate. Please remember do not scrub everything at once or you may kill your "good bacteria" and you will have to start cycling all over again. So if you clean gravel too well, do not change filter sponge and vice versa.... Filter sponge keeps good bacteria so it's ok to rinse it but preferably in the water you just drained from your aquarium, not by running water. You can find lots of useful articles about that on the net.
I don't think your thermometer is faulty, you probably just have "hot" and "cold" spots. It can be fixed with adequate filtration/water movement. Sometimes it's as simple as a proper positioning of your filter and heater to create flow. Your dividers may make it slightly harder, but I'm sure some people figured the perfect way to fix this so yet again - google it.
As for food, my boys love hikari micro wafers. I feed them 2 pellets in the morning and 2 at night, one day a week no food and once every few days they get treat in form of blood worms or daphnia.
Fish has a stomach that is same size as their eye and they will eat a lot until they can not eat no more. They are like little piglets so do not feel bad if they still beg for more. do not give in, or you may do more harm. If your bettas have nice size round tummy you're feeding just right. I hope you will have lots of fun with your new family members.
And what names did you give them?