Yes, little chicks can fall in and drown! It's not really a good idea. I once had a broody hen that took her chicks a long ways from her coop (and little waterer) up to another coop where adult chickens were. She taught her chicks to drink out of the bucket, and I found one chick in the bucket drowned before I caught on to what was happening. So sad. Switched watering system until all the chicks were adult size.
Sometimes I have put a huge rock (or something) in the bucket so the bantams can always get out if they fall in and I also place a cinderblock next to the bucket so the bantams can stand on it. Never a problem with adults.
I keep one of the gallon waterers with the red thing around the bottom and set it on bricks to keep it up out of the dirt, etc. It's usually good to keep a waterer at a little lower than neck level because chickens don't have a way to keep feed inside them. If they bend way over, the contents of their crop can leak out into the waterer and get it dirty. If the waterer is at about chest level, then the water stays cleaner. It's harder to keep the water at the right height with chicks because they just keep growing and keeping the height correct is probably more work than just changing the water.
I sprinkle baby grit on the feed itself. I put it on like I would pepper (if I really liked pepper) in the top of the feeder each day. I've been doing it like that for years with what seems like good results to me. I usually mix it a little with a finger because I have seen some chicks just going along eating all the little granite grit. By the time they are about 14 weeks and looking really adult-like, I just put the grit in a separate container so that they can eat as much as they need. I have no idea when it is that they are capable of regulating their own grit consumption ... other than mine seem fine at about 14 weeks.
Picture from Fleming Outdoors of the kind of waterer that works for me and chicks. Fleming Outdoors is a sponsor here so I guess it should be okay link to them. (We'll see if it works.)
www.flemingoutdoors.com/1gapofo.html