Can i lose 20lbs in about 2 months by doing this and eating this?

This sounds perfect! I lost 20 pounds doing less than this as far as activities are concerned, so you should be just fine. Just remember to drink plenty of water, water is more important for weight loss then most of us know. You got the exercise and eating down. Take care and good luck. You can do it just be patient with yourself and focus on your task to stay motivated.