Does it design the pavement?
No. It counts what a set of dimensions requires. The pavement build-up for its traffic, the falls, the drainage and the kerb foundations come from the engineer.
How are the pavers counted?
One paver with its joint covers (length + joint) times (width + joint). The area is divided by that, increased by the waste percentage and rounded up.
Why extra sand and base?
Both lose volume when compacted, so more loose material is ordered than the finished thickness suggests. The allowance is a starting value: take the real one from your supplier.