I'm no expert, but I have a few Cherry Shrimp in one of my 5 gallon betta tanks so I'll do my best...
How do I take care of them?? - I don't do anything special so far. My tanks do have live plants, and a small bit of algae, so they are eating well and growing fast. They all started out small, all of a similar size at about 1/2 inch and now I've got at least one that's clearly bigger and showing a saddle, so hopefully I'll see baby shrimps in the near future.
What do they eat? - As I mentioned, I have live plants and some green algae so they've been eating everything they can, but I also didn't put my shrimp into a new tank so they had some natural food available. I may look into shrimp "food" or they may just enjoy the frozen brine shrimp I already have for my betta.
Do they do well with bettas? - Some do and some don't. The boy my shrimps are in with initially chased and tormented the little shrimp, but they've reached an agreement and he don't bother them now. Doesn't mean he wouldn't eat one if he had the chance.
Do they mind the heat? (bettas heater) - Mine are fine with the warmth.
Do they eat plants? - They don't seem to "eat" live plants, but I have seen then gnawing on the dead/dropped leaves from the Anacharis plant.
Do I need more hidey places (3 in the 5g and 2 big ones in the 10g) - You can never have too many bolt holes and hiding places. I have a big clump of Java Moss in my tank. When in a tank with a betta they need lots of places to hide, particularly when they molt because they're really vulnerable at that time.
I'm sure some experts can give you more advice.