Welcome to the forum!
With wood shavings you never needed that rubber mat. It doesn’t hurt, but shavings give them good traction. The problem is with slippery things, like newspaper or maybe the bottom of that plastic container. The shavings need to be deep enough they don’t scratch them all away.
Chickens scratch, they scratch a lot. And they have power when they scratch, even baby chicks. Scratching is just what chickens do. To reduce the bedding getting into the food and water, raise them up out of the shavings. If you can get them up to about the level of the chicks’ backs you can help yourself a lot as far as shavings in the food and water. It won’t stop it but it will help.
I need a little more help before I can give you a time they can go without heat. Where are you brooding them, in the house or outside? What temperatures are you talking about, highs and lows? Are you exposing them to cooler temperatures, maybe by taking them on excursions outside where they can peck at the ground and grass? There will be a difference in my answer if they are in your house with an ambient temperature in the upper 70’s versus them being outside in freezing temperatures.
I raise mine in an outdoor brooder. I keep one area warm enough in the coolest temperatures but let the far end really cool off. My full-sized fowl chicks have no problems with temperatures below freezing and no supplemental heat at five weeks of age. If they had been kept in a tropical climate with no chance to acclimate, they would probably need to go a bit longer.
The best way to tell how you are doing with heat is to watch the chicks. If they are too warm they will get as far from the heat as they can and probably lay around and pant. If they are too cold they will crowd under the heat and probably give a plaintive chirp. When they are OK with the heat they just roam around.
I’ve raised chicks with broody hens and in brooders. That 90 degrees and drop it 5 degrees a week is an extremely safe method. But I find they can usually handle much cooler temperatures than that gives you, especially when they get a little older. The first three days or so they tend to spend a lot of time under a broody or in the heated area. After those first few days they do pretty well in cooler temperatures.
If yours are in the house, you can take the heat away and see how they respond. If they get cold, they will let you know by crowding together and giving a heart-rending chirp. If it suddenly goes dark and they have never been in the dark that change can upset them too. In that case chirping doesn’t mean they are cold, just that they don’t like that change to dark. But they will soon get used to that.
Chicks raised by a broody hen do not have access to food and water 24/7. Some people raise chicks in a brooder but with an alternative heat source that does not provide light. Those chicks are in the dark and not eating or drinking whenever it is dark. It doesn’t hurt to have food and water available 24/7, but it is not necessary.
I’ve been known to use something like this. The platform is an inch or so above the bedding and the container is a bit above that. They can easily hop up there and drink. With young chicks I fill the bowl with rocks so they can walk on water and not drown. In a warm brooder it does not hurt them to get a little wet. You could do something like this for food too.
