If i starve myself for 2 months and only eat like a carrot a day and lots of water and work out for about an hour will i lose weight How will i keep it off after the starving?

I would not recommend you do this. You should consult a medical professional about your concerns and they can hook you up with a dietician who can help you decide an approach that works for you. It is dangerous to go two weeks only eating a carrot a day. You should know that you can lose more weight if you eat three meals a day and your body can learn to keep off the weight. What will happen if you don't eat is that your energy level will bottom out and you will find easy things to be very hard. Your body needs nutrients and proteins along with sugar to produce ATP or energy. I do not recommend this method.