Have you reviewed the IFIXIT guides? Each one has a difficulty rating so you can gauge what maybe beyond your skill level. Check out the videos as well before you start.
Generally taking the display unit off is not overly difficult as long as you take your time and don't force things.
As for dust, if you are doing this in the middle of a four mill dust would be a problem ;-}
I would make an effort to clean the area fully of any debris and put down antistatic lint free cloths to rest the display on in a safe place while working on the system (making sure to follow proper ESD guidelines), then carefully cleaning it before re-assembling.
As for dead pixels you won't create them in the repair process.
I think your just nervous here as this is your first computer repair. Thats a good thing! As you'll research things out fully and make sure you have the right tools and setup before attempting.