Is it true when you use alcohol the automatic functions of the body controlled by the brain like the heart in the breathing also become impaired?

No, it doesn't have a direct effect on the autonomic system. It's effect is directly on the organs it goes to. It travels to organs by way of the circulatory system.
Alcohol that is not processed by the liver goes to the heart. In the heart, alcohol reduces the force of heart contractions. Consequently, the heart will pump less blood, lowering overall body blood pressure.
Alcohol is known to make blood less likely to clot, reducing risk of heart attack and stroke and alcohol dilates blood vessels.