It appears that you're new to microcontrollers.
"Arduino app 1.8.6"
You're probably referencing the Arduino IDE version 1.8.6 archive (made for either Linux, Windows, or MacOS). This is a whole directory tree of files including: integrated development environment/editor, cross compiler tools, C/C++ source code for base functions and some optional libraries (supporting hardware such as LCDs, stepper motors, servos, WiFi, etc.).
"Is there a way to print the contents of the library?" "...see all of the 'commands' ..."
Consult the reference manual on what functions are available to call when writing your "sketch" (the C/C++ program to be uploaded to the microcontroller). See "Language Reference"
here. Each optional library will have their own reference documentation (same link). Also see the "Variables" and "Structure" tabs (under "Language Reference") to get acquainted with the C Language parts and
here on how to upload your sketch to the Nano. You can also consult any C/C++ Language book/tutorial. Unfortunately, I haven't been able to find documentation on the avr-gcc Standard C and math libraries included (they're here: /arduino-1.6.8/hardware/tools/avr/avr/lib/libc.a and libm.a).
"Nano module"
Is a hardware implementation (board) containing a ATmega328 microcontroller (schematic
here). There are many boards in the Arduino ecosystem. See
here for their current and past lineup. Their original, popular "UNO" board has an ATmega328 microcontroller from Atmel (now Microchip). The Nano is a smaller form-factor version of this. The newer boards may have faster, different processors with additional peripherals (eg. WiFi). The idea is that all boards can run basically the same sketch but with different references to pins or peripherals specific to the board the sketch is uploaded to.
"mine had the chinesium CH341 Comm chip"
It's likely not a genuine Arduino brand board. But that's okay. I would expect it to behave like a genuine Arduino Nano.
Seek out Nano or UNO sketch examples/projects on the Internet.