I suggest you look at height to weight ratios, google it and download a chart.
Yes, light yoga is fine, some extreme yoga should be avoided. Headstand, shoulderstand are ok. The idea is to conserve energy that can be used by the body to heal and clean.
A long fast is any where between 20-40 days. I personally do not suggest 40 day fast. A complete fast is when one feels the true hunger. There are cases when people have felt true hunger in 15-17 days. This is affected by lot of factors, but primarily healthy individuals get to the true hunger stage rather quicker than those who are not that healthy.
I prefer 30 day fast, 30 day feeding, 30 day fast if you need it.