They have no powers, they are simply well trained in hand-to-hand combat ala Batman.
Because Big Figure wanted to cut through the lock so he could get to Rorscach before the prison riot was over and order was restored. As you will have noticed Rorschach broke the fat guys fingers then tied his hands together, thus meaning he was in the way of the door lock mechanism. As a result, Big Figure deemed it quicker to simply cut him away, as opposed to trying to untie the knot.
Did he die? The film gave no indication that was the case, it certainly showed him falling onto the floor. He could have passed out due to shock, the intense pain he would have felt or the sudden drop in blood pressure in his body.
The temperature on Mars varies greatly depending on where you are and time of day. It can reach surface temperatures of 20c.
Either way, do you not think that since Dr Manhattan could create an aura of breathable atmosphere around Laurie, he might have been able to create heat too?
Unfortunately the scene explaining where Rorschach got his mask from was cut (which is a shame as it is central to explaining why he chose to fight crime in the first place). Long story short, thanks to Dr Manhattan there were great leaps and bounds in various technologies thanks to his presence. One of these was the discovery of a method to allowing viscous fluids to move freely inside of materials. Hence the funky ass mask. There is a lot more regarding the creation of the mask and Rorschach's origins, but would take too long to explain.
I think you'll find they didn't, if you watch the news reports in the film you'll see that there was great shock around the world at the creation and the presense of a super-human. Indeed, there was one scene where a man says that if you are not afraid at the idea of Dr Manhattan being a walking god then it is an indication you are insane.
If you were a being with control over objects at the atomic level, were able to see reactions at the chemical level, able to perceive time in non-linear perspective, can walk across the sun, teleport between two locations in an instant etc etc etc....If you had that sort of power would you really concern yourself with wearing pants?
Again, due to cuts you do not see the progression of the character as you do in the book. Initially Dr Manhattan does wear a full black body suit to cover his blue wang, but as time moves on and he becomes ever more detached from humanity so he begins to wear less and less.
To emphasise how vulnerable and how powerless he feels without his suit.
No, it would appear you are insecure about seeing male genitalia and so have to resort to name calling in an attempt to distance yourself from any possible notion that you somehow enjoyed seeing a cg blue penis on-screen. I can only imagine that you spent large portions of the movie sweating profusely, shifting around uncomfortably in your seat, all the time the bag of popcorn shaking in your hand as you deal with the sudden rush of strange emotions and feelings. Seek help. hurrrhhhhhhhh