"the most caudal part of the brain, the is continuous with the spinal cord."

The answer would be medulla oblongata

Medulla is the lowest part of the brain stem which has a role autonomous nervous system. Medulla is important to sustain life as it controls the blood pressure(vasomotor), respiratory system and cardiovascular system. It also controls many reflexes that related to cranial nerves like gagging reflex.

It's cell theory. easy name i would think.

Distillation.  distillation is the correct answer.