Static Electricity Accumulation
How are elevators powered (old elevators, this building is an old one).
  


By electricity. Why do you ask?


  
  Why is there humming? What would humming be caused by that is audible through the wall with elevator power so close by?
  


Humming can be caused by pumps, air-conditioning, ventilators, etc. The vibrations can travel very long distances through the solid building materials.


  
  How would electricity spread through the floor in such a case?
  


It generally doesn't. You give no location in your question or user profile (which is one of the reasons it's there) so we have no idea what the electrical standards are in your country.


  
  How dangerous would jolting electricity through a mattress/carpet be if you were exposed for prolonged periods of time?
  


This is most unlikely. 


It would require a conducting bed frame.
If the bed frame is conducting then it would ensure that all parts of the bed were at the same voltage so you certainly would not get jolts while on the bed.



  
  What would you want an electrician to investigate to determine where the jolting sensation is coming from?
  


Take voltage measurements.


  
  Could the described circumstances be caused by static electricity with polyester carpets, polyester mattress (20%) and generally dry air?
  


Yes.