Will I stop breathing during anesthesia?

It depends. It is possible to breathe entirely on your own during general anesthesia, depending on the type of surgery you have. With some types of airway devices such as an lma, you don't have to be on a ventilator. However, major operations on the abdomen or chest, for example, usually require a breathing tube and the patient does not resume breathing on his own until the surgery is over.
It depends. You may or may not stop breathing during anesthesia, depending on the specific type of anesthesia, the surgery, and your medical history. It is important for you to know that you will not stop breathing until after you are unconscious, so you do not need to be afraid of being unable to breathe while still awake.
Maybe. Some operations require muscle relaxation or paralysis, which also paralyzes the respiratory muscles. In this case the anesthesia provider will provide respirations (breathing) with a ventilator. Other operations may not require paralysis, and you may continue to breathe on your own even while under anesthesia, possibly with some assistance.
No. When you undergo general anesthesia, you are deep enough that you would not breathe without support. The most important duty of the anesthesia team managing you is that you continue breathing. That is why they intubate you (pass a breathing tube down your trachea), place you on a ventilator, and monitor your vitals and other parameters very closely.
Possibly. Depends on what type of anesthesia you receive. With general anesthesia we take over your respirations and place you on a ventilator. With regional or MAC anesthesia you will be breathing on your own. There are risks with everything. When you receive anything other than a general we are always to prepared to breathe for you if you were to stop breathing on your own. .
General Anesthesia. If you are getting General Anesthesia than most likely yes at least for some portion of the surgery. If you are getting sedation than you will breath on your own.
No. One of the main things that anesthesiologists do is ensure that patients keep breathing.