Ok, i will try to answer most of your questions, but i want to keep it somehow short as i am not in the mood for a long post here… sorry.
1: I dont own Arturia Pigments, so i cant tell you a proper answer here. If you want to use the C4 Commander Software (CS for future explains.) with Cubase, then you will need additional software, that provides you a “virtual” midi-cable. Like the one at 2:48 in your linked video.
Sadly this has a downside, because CS does not operate bi-directional. This means if you change a parameter with the mouse inside a VST/Cubase, it wont be reflected by the C4 and the LED-FeedbackRings around the encoders will stay where they are. CS was written mainly to control hardware synths and for that purpose it is really a great software.
2: Yes, the C4 sends CC numbers from 0-31 by default.
No, a push from the encoder sends NOT pitch (nothing from the C4 sends Pitch on default), it sends Note On/Off messages, ranging from Note Number 32-63, depending which encoder is pushed. In general you can add +32 to the CC number that is used, to get the Note Number. For example, if you push the first encoder in the top row (which is CC number 0), you simply add +32, for the Note Number.
3: The reason for that behaviour is, that the encoders use relative values, instead of absolute values, that most software expects. So a single tick to left or right with the encoder is a ± 64 step, instead of a ±1 step, that is expected by the software. This results in a switch like behaviour, where you can only have either “1” or “65” as a value, but nothing inbetween or over 65, as the next step would exceed 127 (65+64=129), which is the highest value available for absolute values.
4: This works only, because the third row of the encoders from a C4, have the same assignments like the encoders from a MCU Mackie device (The devices that have faders and only one row of encoders and only one display). The Mackie device from Cubase was never meant to work with the C4 (sadly). It is simply coincidence that these encoders work. You should avoid using this Mackie device at all.
5: I dont know your setup, but i assume your “mirroring” from Mackie device to Pigments is still active.
6: No, the C4 can work standalone. You dont need the CS software to work with the C4. You would only need it for the solution, i mentioned above.
What you want to achieve by using your gear:
1: I am sorry, but i dont exactly understand what you wrote here. If you want the same like in the video, then you will need the CS software and a software that provides you with “virtual” midi cables. Mind you, that this video is cheating you a little. This solution dont work bi-directional. The guy in the video never shows what happens if he moves/turn something in Pigments software, but i bet my ass that it will not be reflected on the C4. The LEDRings around the encoders will not show the actual values. Although it seems to me, that this guy does not really know, what he is talking about. He mixed so many midi-terms wrong and described his actions very, very poorly.
Anyway, you need to understand that the only reason he used the CS software is (he although mentioned that without it, the whole thing would be a another story 
) to convert the relative values of the encoders, to absolute ones and these values are send through the “virtual” midi cables to the Pigment software. So the CS software + the “virtual” midi cables work like a “inbetween” software for the midi-communication. This solution works, but only in one direction. If this is enough for you, then you might get it to work. For me, this is only a half baked solution and more of a hack then a solution. Not nearly close to “full potential” of what the C4 offers, but better then nothing.
2: You cant control both VST and hardware at the same time. This is not possible with this solution. You need to switch from either VST or Hardware, but not both at the same time.
Last words:
Dont be frustrated by the C4 device. In my opinion, it is the best midi controller outthere in that price range. Sadly it is not a “works out of the box” thing. You need to know how it operates.
If you try the new invented midi-remote in Cubase 12, you can use at least the encoders without any big problems, but to use the LED-Rings and the display, you will need to use the API from the midi-remote and program it with JavaScript. There is at least one script for the C4 ready here:
This script controls the EQ´s of banks with eight channels at once. It is a good showcase, of what you can do with the midi-remote and the FULL potential of the C4. It works bi-directional with LED-Rings and displays.
Although @Martin.Jirsak and myself are working on a C4 script, that will offer way more and is working more or less like a Mackie device. I just cant tell you, when it will be finished as @Martin.Jirsak is the master here .
Hope i could help.