I really don't know about the first two. but wanted to throw this out..maybe the inside casting of a shell animal of some sort, fossilized. I have found two somewhat similar to yours, much smaller though. I thought they were pottery, they looked so deliberately formed. Then saw an ID of an internal cast of a shell...what the critter's inside chamber was shaped like. There was a break in them just like yours. Not a connected ring...Hope someone can say for sure!
The round pieces look to be a Bone from a cut piece of meat, like a ham. Modern and cut with a meat saw.