These have all been answered multiple times all over the internet:
1. To see thestrals death had to be seen and fully understood. He was too young to remember seeing his parents die, and he didn't witness Quirrell dying because he blacked out. Cedric was the first person who died right in front of him that he was old enough to remember and fully comprehend, so that's why he couldn't see the thestrals until after Cedric's death.
2. That has got to be one of the most idiotic question I've heard about HP. No offense to you, at all. Everyone asks it as if it's some great big mistake that JK Rowling made...but really, who's handwriting hasn't changed since they were a teenager?! My handwriting has changed significantly since I was in school, and so has everyone else's that I know. Plus, with how much Snape has been through since his teenage years, becoming a death eater, losing the woman he loves, working for Dumbledore, being a double agent, etc., his handwriting is bound to change, as handwriting often changes after big, stressful, life-changing events in your life. He has grown and evolved with him, and so has his handwriting. That's why Harry didn't recognize it.
3. His room was a cupboard under the stairs at first, no windows. One he got Dudley's old room, I figured that Dumbledore and Hagrid just wanted to mess with the Dursleys a bit. I've always pictured Dumbledore and Hagrid having a great big laugh as all of those letters came tumbling into the house from every orifice!