You can go without food for a month but you would become very weak. You wouldn't get the nutrition you need and you'd become tired all the time. Although you can go long periods of time without food; I wouldn't advise doing so. The consequenses probably aren't worth any of the benefits. And you'd have to drink more fluids to make up for some of the fluids your losing from your daily amounts of food that contain them. You can only go three days without water/fluids.
Depends on your environment and state of health. Most healthy people can survive a month without food assuming there are no other significant stresses (exposure to elements, disease). Protesters who go on hunger strikes have survived as long as 4 months on little else but water.
Any time you go more than 3 or 4 days without food is dangerous; you body goes into ketosis and possibly ketoacidosis which can be life threatening.
Yes it is possible to stay without food for a month, even longer but you can't live without water for more than 3 days.
But the question does not mention water deprivation, only food deprivation.
No, without ANY food or water you wouldnt survive a month.