Reading the SWO information via Serial Monitor plugin in Visual Studio. 
Is that the complete information?

In order not to loose the whole stuff I spent hours to reproduce which BMP compilation I had used.
The only one that worked like I described above is this:
https://github.com/blacksphere/blackmagic/releases/tag/v1.7.1
I managed using Mingw32 to compile to a single blackmagic file and uploaded to the Blue pill using Cubeprogrammer. (I changed the Com port after upload and USB connection to that small number but that was not necessary, I had read that that also could be an issue)
Connections:
BMP: PA3-->Target BP: PB3
         A5                    SWCLK
         A14                  SWO
Does this answer your "one more Question"?

Using the BMP bin files you refer to doesn't work!!!
Blink in Arduino always yields mismatch at some address. 
That BMP.bin I finally used (see my link above) runs smoothly also in Vmicro.... 
Will be sticking to that, of course.
I used Generic STM32F1 series with submenue and the SerialWireOutput library with the example provided.

Is it possible to access the CPU registers?

Does BMP only work with that core? My application needs the Maple core.

Anyway, do you need shuffling the Boot0 jumper and "attaching to process" with those BMP binaries? 
With my compilation it runs through fine (debugging) when leaving Boot0=0.

Main question: How to view the GPIO (Port) registers?
In CubeMXIDE they are called "SFR's" if I remember correctly.

Furthermore, on a fresh installed Win10 notebook neither Arduino IDE works  nor vmicro using the BMP with the same settings as in the main PC.
"Com10 port (being the GDB Server port) not found" -

Update: On the notebook PC I installed Mingw64 (don't know if essential for this issue).
Uninstalled Arduino. Loaded Arduino (portable). 
Deleted Arduino15. Started Arduino. Installed Due from Boardmanager. Installed STM32F1 boards (STMduino).
Result: Blink compiles with BMP and runs in Arduino and in vmicro without needing the reset button.

But, what about port register viewing in vmicro? Visual GDB needed?

There is nothing specifically for this purpose in the hardware debugging at present, and we will look further into this.

To my knowledge the e.g. GPIOC register is resolved to a memory address at compile time, so this can be viewed in GDB, once the address is known using 'x'

There is a Digital / Analog Pin Viewer built into the vMicro Serial Debugger which allows the digital pin states to be altered, and analog pins graphed.