Fluval Edges are 6g.
Don't add a betta; you will have to lower the water level so he can breathe and also he WILL eat your danios & rasboras for sure.
Cories also like to gulp air so personally I would not do.
There are many varieties of dwarf shrimp that would be fantastic in your tank... Red Cherry Shrimp, Crystal Red Shrimp, Emerald Green, Pearl Blue, Gold Bee, Blueberry... the list goes on. There are a few retailers on the web, like shrimpspot.com which offer a good pictoral catalogue of shrimp.
Some othe fish you could try are
-African dwarf tetra species
I STRONGLY suggest you purchase the book Nano Aquariums by David E. Boruchowitz
... I stumbled upon it of my library and in addition to awesome info about setup/maintenance of nano tanks it has a really good guide to nano-fish complete with pictures, making it an awesome book to flip through if you are simply looking for a cool-looking fish to put in your nano tank.