How is it possible that Rorschach does not get hurt after several gunshots? He might be wearing a bulletproof vest, but this would make him look bigger and not so agile.
No so. He's wearing a trench coat, and many bulletproof vest are easily hidden under a large coat. He could have one, or even something made by Nite Owl II (like his grappling gun), but no. The Rorschach wouldn't wear one.
If he's not bulletproof - why would he risk getting severely hurt (or killed)?
Because the Rorschach has a death wish. Which is why he doesn't wear armor, or use a gun liberally. Why he has no problem taking on multiple people at a time. He wants to die, but doesn't want to commit suicide. This is also why he doesn't flinch at the cop aiming at him.
So given that he doesn't have armor, how did he survive? The cop simply missed.
Look how dark this apartment is. And it's movie dark, in real life it would be much darker. You can't barely tell where Rorschach's legs and arms are, outside of the flashlight. Once the cop puts down the flashlight, he's basically aiming blind. He misses. Rorschach gets confirmation that the cop is useless, so he jumps and moves on.
Also keep in mind that Rorschach is a legend, a myth, a boogieman in the masked hero world. The cop was scared. His partner was hurt and a murderous vigilante is standing at a window staring him down. Later in the film, 5 cops freeze up when they see Rorschach.