Question

which part of the brain controls respiration process?also heart beat and peristalsis?

Answer 1

Respiration is being controlled by breathing center in the lower part of brain stem, called medulla (medulla oblongata). It is the most evolutionary old part of our brain which controls automatic functions and contains centers of unconditioned vital reflexes (vomiting, coughing, sneezing, swallowing). That's what controls breathing, heartbeat, peristalsis, etc.