Hua hin is widespread with many different types of locations, from City to rural living, spend your time wisely looking at all areas as a 3 week vacation is very different to full time living, here's a guide to Hua hin which may help you
Sounds good but do it within the first 30 days, go to the main immigration office in Thap tai and speak to the lady on the front desk who speaks English, it's easy to do yourself if you take your time and follow the procedure.
Ok you could do it on just over 1000 baht a day but that will be just living basic in cheap accommodation and eating local food but you will soon tire of that, again it depends where you are, The North (Issan) area is nice and more affordable.