Okay, I hate being the nah sayer but
here it is Nah!
As already mentions the effect of caffine will be multiplied and cerrtainly will not help the fast in any way.
You can have what ever you want you are in charge. a 20-30 day fast is never recommended with high energy output.
Yes by all means move stay as active as your body is willing. But listen to your body first.
As for Hair loss, well that is a very individual thing.
I loss a lot, far to much.
not during the fasting days but shortly after.
Any drastic shift in metabolism can cause this.
I stopped in for a trim and a hair dresser asked me if I was having cancer treatments.
Just the facts.