You’d have to lose just over half a pound every single day. Half a pound is the average daily loss on an extended fast, once the big water weight losses finish. So, sorry to say, I don’t think it would be possible, even if you fasted all 113 days until the 1st of June. Which I really hope you, or anyone, doesn’t try, even with medical supervision.
But that doesn’t mean I’m trying to discourage you, far from it, any loss is a gain in fasting.
As for hair loss, I’m a balding man so my advice might not be the best, but I refeed with a lot of meat, eggs, and maybe some fruit, and hair loss has not increased beyond the regular yearly rate. If you like I can show you how to comb it over so no one will notice (joke).