Hey Skiweeangel,
For your first question, a ten gallon would be plenty space for Red Cherries, to live comfortably and breed. Cherries are a very hardy, perfect for first, type of shrimp. Hard to kill, will live in a wide range of conditions, and will more then likely breed.
Filters, it depends how much water current you personally want. On some of my shrimp tanks I use HOB Power Filters, rubber band some nylon stocking around the intake, and works great. For less current, and ease, I'd suggest just getting a sponge filter, typically used by shrimp breeders.
Food kind of depends on what your shrimp will eat. I had some shrimp they wouldn't touch flake food and had some that loved it. I don't know why even if they were the same shrimp in different tank. So I'd say keep a variety. They commonly like broiled veggies, bottom feeder sinking pellets, and algae wafers.
I don't really know what you mean by prolific, if it's like personalities, they don't have much. They just are really peaceful, scavenger the plants and ground for food. They are workers, pretty much.
Other tips, try to look into live plants, they love 'em. Java moss, hornwort, and naja grass aka guppy grass, are common plants they use low light, and are typically found in the common shrimp tank. Also watch out for liquids you add to the water, if they have high amounts of copper or have a warning to say not to use with invertebrates, don't use them.
Anymore questions feel free to ask, I've been keeping shrimp for many years now.
Peace,
Ben