The rubber-coated pickup pads and rollers are considered maintenance items and you are supposed to replace them on a schedule. If these are no longer available I've had luck smearing some rubbery glue over them in-situ very thinly after wiping them down with alcohol. I use a polysilane glue such as G02 Glue or Elmer's Stix-All Cement but don't see why a normal solvent-type rubber cement such as E6000 wouldn't work. The glue trick works better than some new aftermarket rollers!
Plastic gears are supposed to be self-lubricating and the noise is from them wearing down creating lash. For example with the HP4250/4350 you have to replace the plastic swingplate gear every 225,000 pages, which is also when the roller maintenance kit is due. The teeth get pretty visibly worn and cause a huge racket long before they are worn out so the noise is just something everyone with one lives with because after decades of use it's still so reliable, at least out to about 1 million pages printed.
If operation is affected by paper dust covering everything to require frequent cleaning, then you really ought to look at using some different paper.