I found this a few years ago while planting trees, looks as though it's being used for some sort of grinding, also there's signs that it's been in a fire. Why has chalk being placed in it? Size 7 cm square x 4 cm high
It appears to be a naturally worn/chipped piece of flint. It may well have been in a fire. As for the chalk flint is found and formed within the chalk thus explaing the chalk. A good tip for identifiying a flint tool are thin flakes that make depressions in the rock. These depressions will look like the imprint of a fossil shell but are just the way flint flakes. A sharp edge with tiny chips may also signify a tool.
No, no - looking at your third photo, it is a fossil bagel !
...Complete with cream cheese, but without the salmon.
Humans have evolved to recognize patterns. It helps hunters spot camouflaged animal prey, gatherers to distinguish a poisonous fruit from a good one and get a feeling for seasons, and everybody to find existing friends in a crowd, avoid enemies, etc. Given only a slight pause for thought, we can't stop ourselves assigning significance to shapes and colours of things - be they clouds, the yoke of a fried egg, scorch patterns on the Turin shroud, or many another thing - including flints. Sometimes we are right. If we are wrong, that helps refine our skills. Whatever; it does no harm to observe, wonder and find out.