This is my first time raising chicks.

Glad to have you here. I have been raising chicks, on and off, over 30 years and I always get too concerned about the baby chicks. You are not alone in concern for the little ones.
My question is, can they over eat?
No. I leave feed and water in the brooder 24/7 the entire 8 weeks I have them in my brooder. Never had an issue with a chick overeating. Don't know if it's even possible. If you leave food and water in the brooder 24/7, then the weaker chicks will not get pushed aside by stronger chicks if you had only limited feeding. Open feeding makes life less stressful for the chicks.
I am feeding them 20% starter feed and crushing it up a bit.
I don't think you need to crush starter feed. I never have crushed my starter feed and it's never been an issue.
I was leaving it in the brooder all day and night but the chicks crops seem to just stay full all day long. I leave water in the brooder all day and night as well.
Yes, leave food and water in the brooder 24/7.
All 6 chicks are pooping and I have had to clean some poopy butts almost every day for at least one or two chicks.
OK, I don't want to split hairs on termonolgy here, but a poopy butt is not something to worry about. It's a pasty butt that has dried out and is blocking the chick from pooing that you need to watch out for in the brooder. Almost all the time, a "poopy butt" will resolve itself as the chick runs around and/or preens itself. A pasty butt needs intervention by you.
A few other thoughts come to mind after reading all the responses. I use red heat lamps in my brooder and they stay on 24/7. The chicks don't have any problem sleeping under red lights.
Although you don't need grit for starter feed for your chicks, I was advised by a lady who raised chicks for many, many years, that it is still best to provide the chicks with fine grit just in case they eat some of their bedding. I live on a lake so I just use sand from the shore, but there is also bagged commercial fine grit for chicks and it does not cost much. I put some lake sand in a small container, and my chicks started dust bathing themselves in it! Very cute. But I also caught them eating some sand and I guess that is a good thing. It certainly won't hurt them.
At about 6 weeks, I will dig up some small clumps of dirt with grass on it from the chicken run and put it into the brooder. The chicks usually run away from it at first, but then they start to pick at the grass and scratch at the dirt. I was told that is a good way to introduce them to their eventual outside run. Also, around that time, I will start to give them small samples of kitchen scraps I feed to the grown hens. Consider it as a treat and not a replacement for starter feed which they need. Do they need small clumps of grass and bits of kitchen scraps? No, but I think it helps my chicks get used to the idea of what is coming for them soon, and they seem to enjoy the variety at that point in their lives. If they were with mama hen out in the chicken yard, they would be introduced to that stuff much earlier.
I have never used the heating pads, or tents, or momma hens warmers, etc... I have always use red heat lamps for over 30 years. It works for me, so I guess I won't change. In any case, I start my chicks off at 95F for the first week and drop the temp by 5F every week in the brooder.
I live in northern Minnesota, and when I brood my chicks early in the spring, it still gets down to 15F in the garage at night. So, I actually have 2 separate heat lamps in my brooder. I don't want to come out in the morning and find frozen chicks because something happened to a heat lamp overnight. I also put a remote thermometer in the brooder and set a low temp alarm to sound in the house if the temp in the brooder drops below my set limit. Helps me sleep better at night for those first weeks when the chicks are so small.
I hope you enjoy this period when the chicks are so small. Take lots of pics because the chicks grow up fast. It's nice to look back on their progress. I make it a habit to snap some chick pics every week of their development in the brooder. And feel free to upload those pics to the BYC forums because we all love to see those baby pics! Best wishes.