Hey Jerry,
I would also ground the X and Z axis. As you can read in this spindle manual:
Ground the machine in accordance with the regulations!
The machine in which the motor spindle is installed must be grounded separately for each moving machine component. Even if, for example, the moving axes of a milling machine are electrically conductively connected to each other via ball screws and linear bearings, this electrical connection is insufficient for the protective earth connection and must be supplemented by a separate earth connection for each axis in accordance with VDE regulations. A protective conductor test must be carried out individually before commissioning.
– Source: Mechatron HFS Series High-Frequency Spindle Operating Manual
Some of the questions you ask suggest that you haven’t read the VFD manual all the way through. I admit, not every cheap Chinese spindle has as good a manual as the Omron MX2 (PDF) / Hitachi WJ200 (PDF) VFD manuals, but I’ve looked at all the Chinese VFD manuals I’ve come across, and grounding was always described.
I also see that your VFD is not installed in a grounded control cabinet and in addition is lying on its back. The VFD manual should state that the VFD should not be operated lying down for ventilation reasons, and that the unit is intended to be installed in a grounded control cabinet, e.g. like said here in my VFD manual:
Caution! The equipment is intended for installation in a cabinet. The end application must be in accordance with EN 60204-1. Refer to the section “Choosing a Mounting Location” on page 29. The diagram dimensions are to be suitably amended for your application.
– Source: Omron MX2 User’s Manual
Also, a loose VFD means that the cable ends are subject to movement, and this is not good because there is normally no strain relief. After all, such devices are intended for fixed mounting. I see you fixed the cables to the VFD at some points, so it’s not loose, but I would not consider this really being a good location for mounting a VFD. I would expect it to be mounted at a height where I can read the displays and operate the device when standing in front of the machine. Also usually in the door of the control cabinet, your find the Power Switch, the Emergency Stop knob and the Reset knob of the installation at that height.
The spindle cable shield should always be connected at both ends. At the spindle end it should be connected to the connector housing internally, and the connector should not allow it to be connected any other way. Here you can see how the cable shielding is connected inside spindle connector (figure 3, see “PS2”).
I would not recommend anyone to connect a spindle and a VFD themselves who has not acquired at least the part of an electrician’s knowledge necessary for this purpose.
Furthermore, I would not recommend anyone to connect a spindle cable without having read this document carefully:
Even electricians usually have not this knowledge since it deals with shielded power cables.
If the hose is plastic, this is useless. See here:
I’ve linked the moment in the video where the author gets to the summary, but of course it’s worth watching from the beginning.
If you get electric shocks from static electricity from your dust hose, you can however cover the areas you usually touch with copper tape or aluminim foil and ground it, so you don’t get the shocks anymore, but basically you can’t ground any non-conductive material itself. All the instructions about this you find in youtube are nonsense.
Here you can see that even though the PVC pipe is wrapped with grounded wire, it still attracts paper scraps when it is statically charged.
I don’t know which screws you exactly mean, but how to ground the VFD should be described in the manual of your VFD. I can’t insist enough on this. Read the fine manual! 
Here I have covered the topic again.
Under no circumstances should you connect a self-wired VFD/spindle assembly to the mains without it being properly grounded! An electrician should be consulted for this.
In many cases, the grounding of the VFD is connected to the metallic part of its housing, but you have no guarantee that this is the case. Usually the ground symbol (⏚) is the grounding point of the VFD.
A VFD is designed to be installed in a metallic grounded control cabinet, such as the one shown below. Such a cabinet has a steel mounting plate that you can remove and mount the VFD on, and the whole enclosure is grounded.
Usually it’s not only the VFD that finds its place here, but also many other things you probably want to use.
How the VFD is connected to ground is described here in Figure 2. There you also find the answer what to do with the VFD end of the spindle cable shield: It should be clamped to the mounting plate with a cable clamp or grounded with a grounding cable gland.
Basically, all the ground wires should converge in one point, and that’s in the control cabinet usually at the one screw of the metal housing part of your VFD, which is also marked accordingly (⏚).
If the metal part of the housing of your VFD is not connected to its ground terminal internally, then you should run a ground wire from this ground terminal (⏚) of the VFD to the steel mounting plate by screwing in a ground connection lug there as close to the VFD as possible, and run all the ground wires together there. From the ground at the VFD on the mounting plate, the ground wire in the power input cable goes to your wall box or your room’s electrical panel, and it’s also from the ground at the VFD that the ground goes to the spindle (the yellow or yellow/green PE wire) as seen below.
Note that even if PE wire and cable shield are both connected to ground, they serve two different purposes. PE is crucial for electrical safety, and shield cannot replace the PE wire.
If you bought a cheap Chinese spindle, you should also be sure that in the spindle the PE (fourth) pin of the spindle socket is actually connected internally to the spindle housing, as seen here. You can check this with a multimeter (set to ohms/resistance, the resistance between the PE wire and the housing of the spindle must be close to zero).
Did you buy a ready-to-use spindle cable? Isn’t the shield already connected inside the spindle connector?
Then it is likely that your spindle or your spindle cable is not shielded sufficiently. The VFD, the spindle and the spindle cable are sources of heavy EMI, because the currents the VFD produces are not nice sine waves. Therefore it is necessary to enclose all of them into something that shields (shielded cables, grounded control cabinet, connecting spindle’s housing to ground). Be sure that the cable shield of the spindle cable is connected to the connector housing internally at the spindle end, and at the VFD end, the cable shield is connected too. Refer to the document mentioned above (Proper VFD Cable Termination).
I hope this is of help to you!