Check the actual USB chip on your clone. Perhaps it's not actually a ch341, but a similar chip that uses a special driver. Focus on that until you see the COM port appear in the the Device Manager.
In Windows 7, go to Control Panel > Device Manager < Ports (COM & LPT). Plugging in your board should make an entry appear there, that will go away when you remove the USB cable. The COM number (e.g. COM1, COM3, etc.) is what you'll set in the Arduino IDE, Tools > Port setting.
That is at the same time oddly specific and weirdly general. What protocol do you want to use as the interface? What language are you programming the D1 Mini Pro with? What do you have so far, and what do you need help with specifically? How much do you already know about programming the LPC1788?
would you please use three backticks next time you include something like code or an error log.
The code part in question is inside of "esp8266_peri.h", which will be included from "Arduino.h", which in turn will be included before "Music_WEMOS_D1.ino.cpp" or any other sketch will be opened.
This also explains the smiley, as *) will be shown as in this forum.
I downloaded the original code, named "Visualizer_Program.ino" and compiled it with no error. I also suggest to post your code here ( please do not forget the backticks ). Maybe we can help then.
Do you have a multimeter or, better an oscilloscope to see what is actually happening between that charging module and the battery shield? Can you measure the voltage and current that it is giving? I suspect the LED is not really blinking, but instead the battery shield is simply resetting due to inadequate or noisy power.
Scanning will crash the shield, as will anything that doesn't send exactly 4 bytes to it. It will also crash on its own when not talked to for a while. When it crashes, it pulls down the SDA and SCL lines, so it becomes impossible to communicate with it or any other device on the same I2C bus.
As far as I know there is currently no fixed version of the firmware available. I did attempt to work on that a little (as you can see on the website you linked), but my lack of experience with the platform makes this difficult. I also asked several more experienced people for help, but they are all busy with the projects of their own or their day jobs -- they did promise to look into that within a few months, though, so there is hope.