When I try to catch them at the LFS for other people, they tend to crawl around out of the water and even jump sometimes. I would definetely have a cover on the tank.
Unlikely unless you starve them. This applies to even dwarf shrimp. I have had a crystal red shrimp eat a baby snowball shrimp before. I don't feed that tank, ever. So food source in there is probably scarce but enough for them to live off of. Although, I do feed them more often now