How do speed based PAS levels work ?

The PAS is just a sensor. Each time a magnet passes the hall sensor/s it switches on or off the 5v coming to it, so the signal wire pulses with 5v.

The microprocessor in the controller (CPU) has logic that can check that input as pulsing or not, so it's a yes or no.

There are other inputs to the cpu that tell the controller what level you've selected on the control panel. The controller CPU has locic that creates a number from that selection from say 0 to 256. It then uses that number to decide how much speed to allow in proportion to that number, so 256 is maximum speed and 0 is none. With a 5 level control panel, that's 5 numbers and 5 different speeds. The throttle works the same. It gives out a voltage from 1.2 to 3.8v. Those 2.6v are devided up into 256 steps, so whatever voltage it has gives a proportional number that is used to decide how much speed to allow. The logic is therefore fairly simple because you can use the same number for each. Additionally, the CPU can have additional code to shape the power algorithms. they can ramp up and ramp down the power or do anything else the programmer wants.

In principle, current control works the same, except it can't use the throttle speed control algorithms, so it needs additional coding.

The more sophisticated the control system, the more code you need and the bigger and more expensive the CPU, so cheap controllers have simple control systems that can be a bit unfriendly. Expensive ones tend to be better.