This diagram is explains everything beautifully. When a nurse comes and tells you hey doc this patient has blown a pupil here is why! It is a sign of significantly raised ICP.
Note the corticospinal tracts decussate above the pyramid hence any weakness will be contra-lateral and ipsilateral weakness is a false localising sign.
Cerebellar tonsils herniate through the foramen magnum. This can lead to significant effect on the respiratory and cardiac centres leading to irregular respiratory rate.
Herniation of the cingulate gyrus under the falx cerebri. Compression of the anterior cerebral artery leading to contra-lateral leg weakness.