Powering On/Off Quectel BG95 LTE & GNSS module
Those voltages Vnom and VIL refer to the voltages the module outputs at PWRKEY. That's why they recommend using that simple circuit with a transistor, because you need to sink current to activate it.
You just need to connect a GPIO from your processor to the base (where that 4.7k resistor is) of the transistor. That GPIO should be pulled down by default (active high IO), and to turn ON the BG95 module, you pulse that GPIO (you put it high) during 500 to 1000 ms and then down again. You don't need to worry about the voltage output of your processor, the voltage at the transistor base can be 1.0, 1.5V, 1.8V, 3.3V or even 5V, most NPN transistors have a Vbe of around 0.7V, so any voltage higher than that will work.
As for the PSM question, 1V8 power domain, means that pin should see either GND or 1v8, so don't drive it with voltages higher then that. Therefore, don't try to drive it directly from a processor with 3.3V reference voltage at IOs. It's pulled low by default, means that the module most probably has a resistor tying this input to GND. This is saying that if you leave it open, it's ok. Rising edge triggered, it will be started by a transition from GND to a higher voltage.
Their proposed circuit is a simple way to wake up the module, based on a positive pulse at the PON_TRIG_EXT, while guaranteeing you're not putting more then 1.8V at that pin. When PON_TRIG_EXT is low, the DTC043ZEBL transistor is 'open', as well as the WM02P06L transistor, so the PON_TRIG will be 'open'. When you apply some voltage at the PON_TRIG_EXT, this will turn on the DTC043ZEBL, pulling the gate of the WM02P06L, therefore making 1.8V appear at PON_TRIG, this transition from low to high will trigger the module to wake. This means that at PON_TRIG_EXT you can use 1.8V but also 3.3V or even 5V, and nothing will burn.