Yes. There is a condition called sleep apnea which can be due to the anatomy of the upper airway or can be caused by abnormalities in the brain. The latter is referred to as central sleep apnea. Either way people with sleep apnea have numerous episodes each night in which they briefly stop breathing.
Yes. If a patient has sleep apnea, they may stop breathing many times. As the breathing stops, the person wakes up enough to breathe again. These are called arousals. A person with sleep apnea may have many of these arousals which fragments sleep leading to daytime sleepiness. The person usually is unaware of these arousals. This entity is diagnosed with a sleep study and there are treatments available.
It can happen. Some people with sleep apnea do stop breathing for some moments at times.