It gets easier the more you do it. Water fasting should be comfortable and enjoyable. Try doing it for 24 hours, then 48 hours, then 3 days, then 4 days, just keep slowly working up until you reach your goal. You can fast as many times as you want as it is very healthy to do so, as long as you have extra excess body fat to do so. I completed a 20 day water fast week ago. Feel absolutely fantastic from it, and am about to start another 40 day water fast for fat loss and autophagy benefits.
Yoga would be perfectly safe while fasting, unless you are feeling lightheaded. Hot yoga might be a bad idea due to electrolyte loss during sweating. Good luck with your fast! Personally, I find days 3-5 to be the most difficult. After that the only difficulty is boredom!