Most native species will carry the eggs under her tail until they hatch, and some for a little longer. Don't expect to see them deposited somewhere right away. They are fully aquatic (an exception exists, but you'd know it) and should be kept in the water along with the eggs.
The current isn't necessary unless you just like it for esthetic reasons. Crayfish occur in both flowing and stagnant water, and if you find it easier to maintain a low-flow tank they would be just as happy. Plants are easier to grow, and some substrates are easier to arrange and maintain in a low-flow environment. Current is good for some fish though. You might find it interesting to add some minnows from the same creek to that tank (hard to feed flake with that current though).
Algae wafers are just fine as a primary diet for those guys. In the wild they eat primarily plant matter. Given a choice they will indeed prefer meat since it is more calorie-dense, but they don't need it by any means, and I've heard it tends to make them more aggressive. That isn't necessarily an issue with a tank as lightly stocked as that one, but keep it in mind. From time to time they do appreciate a bit of meat as a treat. Anything you would eat is fine for them if it doesn't have sauce on it.
I would suggest, if you were to reduce the water flow, adding a double handful of dead leaves (brown from the fall to minimize the input of chemicals from sap; that way you don't have to worry much about tree species). Crawdads will munch on fallen leaves when there isn't other food available, and it will help ensure there is always enough food available.
Make sure you're not removing shed exoskeletons. They need to eat that to recover the calcium.
Please do not release any of the babies, even into the same creek where you caught the parents. Once kept in an indoor aquarium they have been exposed to exotic diseases, and even if they show no symptoms they have the potential to do a great deal of damage to your creek. You just never know what exotic organisms came with your tropical fish equipment. If you find yourself overrun, they're awfully good to eat, or you can trade or donate them to the pet store which usually stocks them, but never release to the wild.
