"3. How difficult of a challenge is it to build sorting machines, anyway?"
The answer is EXTREMELY DIFFICULT. The problem is that it is a network system. The number of possible connections of different elements with different elements is a mathematical concept called "factorial".
https://en.wikipedia.org/wiki/Combinatorics
Even small factorials become extremely huge fast. Huge like the number of atoms in the entire known Universe huge.
In engineering we have machines that do only one thing well. For example, you can burn wood well. No problems.
If the wood have mercury(button batteries), even small quantities, you have a terrible problem (people dying from cancer near the incinerator), if the wood has pesticides or Teflon or chloric materials you will be creating dioxins which are one of earth biggest poison, making burning extremely expensive.
Just a single button battery can contaminate tons of material or water.
Wet wipes for example have made cost of sewerage to skyrocket.
Humans or living beings have something machines do not have: flexibility.
Something that cost 1 monetary unit to do with a machine, becomes 20, 50, 100 units when you get out of the working conditions of the machine.
The fact is that the cost have been externalized. Make people in Africa or Asia die from our waste pollution. It is a good thing that they start saying no and forcing us to deal with the real cost, so we have to be smart with our waste.
At the end of the day it is not that hard. The US was the absolute champion of waste, invented "the use and trow" concept, because they could do it without dealing with the consequences.