It makes a rustling noise.
As for your suggestions, the first one is incorrect use of grammar but the second is okay. You could also say Would you please shut the door? The would you mind part is really not needed, and can sound redundant or a little insincere. Would you mind really means something like Do you object. Someone earlier suggested "Would you please mind shutting the door", which really means "Would you please object to shutting the door." Sometimes 'mind' can mean pay attention to, and syntax should make the difference clear.
something may be rusty
yes
Creak
creaking
A bus door typically makes a "whoosh" sound as it opens and closes. The sound is produced by the hydraulics and air pressure mechanism that operates the door.
I accidentally dropped my phone, causing it to shut off.
Because when you slam the door the door makes vibrations and sounds are made by vibrations.
slam
It's most likely a degenerative joint disease and you should see your doctor.
Touching a blade will not automatically make it go rusty.