Correct wiring for 3 wire single phase motor

1. and 2.: The terminals 4, 5 and 6 are not to be connected to your VFD. This is indicated by the drawing, as there is no wire "leaving" the interconnected terminals. i.e. those are bridging terminals to build the correct wiring of all windings of the motor.

2. probably yes. Normally PE connectors should be designated by green/yellow, but I've seen it often as only green.

3. Depends from your wiring scheme on your premises. If you have combined neutral/protective-earth connect that to your VFD and your motors PE. If you have separate neutral / protective earth you have to connect the PE to your motor's PE terminal.

4. The PES is for EMC-purposes. It starts at your motor's housing and is connected back to the shielding cabling between the motor and the VFD. It will reduce electromagnetic interference. For this purpose you have to use shielded cables. Is it necessary? Probably you won't get any problems with not shielding it. But others may. So in my eyes not applying the appropriate measures for EMC is like letting my dog shit onto the green of my neighbours. So: just do it and use shielded wires. According to the datasheet your motor cable should be low capacitance (<75 pF/m wire-wire, <150 pF/m wire-shield).

Here is a guess as to what the diagram might be. It might be possible to figure out which wire is which and whether or not this diagram makes sense by careful measurement of resistance. I think I have the L-M-H sequence backwards.

More re resistance measurements etc.

To figure out which winding is which and which speed and voltage taps are connected to each winding, you need resistance measurements that distinguish very small resistance differences, perhaps 0.1 or even 0.01 ohms. If you can verify which wire is neutral and which winding is which, you may be able to run the motor, measure current and estimate speed to help determine the rest. Accurately (and inexpensively) measuring low ohms is a good subject to research.

If you can't find detailed information on the motor, you will also need to guess at the capacitor value. You will be able to find tables that give ranges based on motor power and voltage.

You might consider taking the motor housing off and carefully examining the lead wire routing, the connections to the windings and the winding wire size. Be careful doing that. The windings are somewhat fragile and there may be several washers on each end of the shaft that need to be in the right order. Those tend to stick either on the shaft (good) or on the bearing in the housing where they might drop off when you are not looking (bad). The bearings themselves may stay on the shaft or in the housing.

Without knowing the motor current rating, it may be difficult to know if you have everything right if you get the motor running. If you don't know why this motor was taken out or why the air handling system was scrapped, you don't have any reason to assume this is a good motor.