I feed my Scarlets crushed flake food and they do fine. Though my Badis are F4 and F5+ generation so they've always had crushed flake food to begin with so it's a norm for them. I do treat them to micro worms, scuds, daphinia, black worms, and glass worms too.
As long as your tank is a heavily planted aquarium you should be able to keep 3-4 males in that 10 gal tank. The Scarlets are not shrimp safe so don't plan on keeping shrimp with them. Adult shrimps will be fine but shrimp fry will just be food.
Here's a few clips of my Scarlet Badis: