As mentioned earlier in the thread, the females can store sperm for a long time before laying their eggs. Some crawfish can actually just clone themselves. Either way, those definitely appear to be fertilized eggs.
If you get some more pictures of the crawfish, specifically the top, I could help you identify the species.
For the babies, your mom crawfish will continue to hide like that until they hatch. If you want to raise the babies, it'd be good to have a separate tank with a sponge filter or sponge prefilter on the filter intake. The fry could get sucked up otherwise. You could just put the mother in the fry tank now until the babies hatch.
In the fry tank, there need to be a lot of hiding spaces for the fry. Otherwise they will cannibalize one another.
General crawfish care requires hard water and of course your regular 0 ammonia, 0 nitrites, 0 nitrates. If you have any more questions, just let me know or check out
http://www.reddit.com/r/crayfish