Chicks raised by a hen can be on the ground, there's no problem with that.
I grind up my chick starter in the blender for the first few days because my bantam chicks are so small. I agree with the other comments about wetting the feed...I wouldn't do that for fear of mouldy food. Be sure to clean out your feeder well to make sure you've gotten all the old feed out before you put in fresh. I only put a day's supply of food out for chicks and throw out what's left over at the end of the day, giving fresh feed every morning.
You wouldn't want to feed layer feed to chicks because it has calcium in it. Chick starter or grower doesn't, so that's fine. Your hen won't need the extra calcium, either, until she's back laying which shouldn't be for some weeks.