all of them!
Involuntary reflexes, such as the knee-jerk reflex or pupillary reflex, are not subject to conscious control. These automatic responses are typically controlled by the spinal cord or brainstem without involvement of higher brain regions.
reflexes
The brain stem stem could be called the "primitive part of the brain" because it was the first brain structure to evolve, and is responsible for our basic vital functions like breathing and heartbeat.
Reflexes can be either unconditional or conditional. Conditional, also referred to as 'Pavlovian', reflexes are those that we can develop. They are weak in humans, but can be observed more readily in other organisms. For more information on these, research Pavlov's dog. Unconditional reflexes are those which are innate - we're born with them. Neurologically speaking these typically do not have any nerves passing through the brain, unlike conditional reflexes in which neurons pass through higher cortical areas of the brain. An example of an unconditional reflex in humans is beginning to salivate when we smell something yummy. This is down to our olfactory tracts, which contain receptors which will stimulate a reflex resulting in secretion from the salivary glands.
all of them!
The medulla oblongata is a part of the brain stem involved in these reflexes. And no your eyes will not pop out if you sneeze with them open. Closing the eyes is part of the reflex and you have no control over reflexes.
It connects the body with the brain and it takes care of reflexes and the control of heart rate.
Involuntary reflexes, such as the knee-jerk reflex or pupillary reflex, are not subject to conscious control. These automatic responses are typically controlled by the spinal cord or brainstem without involvement of higher brain regions.
Your question is open-ended, that is, the answer is not limited to, say human bodies. One answer could therefore be, "Sunspot". Sunspots are one thing the brain does not control. Weather is another thing the brain does not control. In a mammal's body, the brain does not control the reflexes of limbs, for example.
because they occur in the spinal cord and not the brain so you don't have any control over them.
Long reflexes
Reflexes are automatic, involuntary responses or impulses. Most reflexes do not involve the brain, however, more complex reflexes have to involve the brain in order to process the reflexes. An example of this would be blinking the eye. This is a complex reflex and it must involve the brain. Also, you must take in the place the reason why reflexes do not involve the brain: because it could cause serious damage to the body. Complex reflexes will not cause serious damage if it uses to brain to produce the impulse.
cerebellum
They are. The previous answer is wrong
brain
spinal cord