I'm a relatively new user of ESP8266, I use some NodeMCU devkit 1.0, official boards, with the Arduino core. I've searched for a solution to my problem, but found nothing, not even someone with the same problem :/
When connected by USB cable only, to the computer, everythin works as expected, in the Serial monitor I see exactly what is supposed to be displayed...
But if I use an external PSU (even if I only connect the GND of this PSU to the GND of the NodeMCU, without connecting +V of the PSU to Vin of the NodeMCU) then the Serial monitor is displaying non-sense garbage (in RealTerm, the Error status LED is always blinking with message "UART receiver framing error"), sometimes immediately, sometimes after a few seconds.
The program itself is still working perfectly fine, it's just the Serial monitor displaying garbage, as in this example:
The GND of the external power supply is connected to the GND of the NodeMCU, and the USB cable is plugged to the computer. I open a serial monitor (tried a few) and I see this:
10:43:01 Fri 30 Sep 2016 CET Paris 24.75°C UpTime = 16 hours, 23 minutes
10:43:02 Fri 30 Sep 2016 CET Paris 24.75°C UpTime = 16 hours, 23 minutes
10:43:03 Fri 30 Sep 2016 CET Paris 24.75°C UpTime = 16 hours, 23 minutes
10:43:04 Fri 30 Sep 2016 CET Paris 24.75°C UpTime = 16 hours, 23 minutes
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As you can see, it worked well for 4 seconds after I opened the serial monitor, and the NodeMCU was running since more than 16 hours with no problems, the program is working fine. It's only when I open the COM port that the Serial issue begins... Also it seems to always finish printing a full line correctly, before going crazy, this is strange.
If I close the COM port and wait a few seconds, then open it again, it will work again for only a few seconds.
I also tried on another NodeMCU, alone (without my RTC connected), with the simplest program (just print "hello" and delay one second), same problem.
I tested, re-tested to make sure, it is as soon as I connect the GND of the NodeMCU to the GND of the PSU that the Serial monitor starts showing garbage, even when Vin of NodeMCU is not connected to +V of the PSU.
I tried adding a 10uF capacitor across Vin and GND of the NodeMCU, but it has no effect. I also tried different values of capacitors, again with no luck.
I also tried baud rate 74880 (I saw this weird value mentioned somewhere else) because I was desperate, but again no luck.
My PSU is a 12V 5A (KY-60W-12-L), with adjustable step down module that I've set to 5V but also tried with 7 and 9V.
PSU:

Step down modules that I tried:

Characteristics of the PSU:
Input:
Input Voltage(V): 180VAC~264VAC
Input Current (A): 0.56A Max
Frequency (Hz): 50Hz–60Hz
Efficiency: 82% Typ(230VACFull Load)
Inrush current(A): Cold star <40A/230VAC
Leakage current(mA): <3mA/240VAC
Output:
Output Voltage(V): +12VDC
Voltage Regulation: +3,-2%
Output Current(A): 5A
Current Range (A): 0 ~ 5A
Rated Power(W): 60W
Start time, hold-up time(ms): Ton≤1000ms,Td≥20ms @230Vac Full Load
Rise time(ms): Typ:20ms @230Vac Full Load
Ripple/Noise(mVp-p): 120mVp-p
Environment:
Working Temperature (°C): 0°C - +40°C(refer derating curve)
Storage Temperature(°C): -20°C - +60°C
Humidity(%): 20% - 90% RH non condensing
Safety/ EMC:
Withstand voltage(VAC): I/P-O/P:1.5KVAC,I/P-FG:1.5KVAC,OP-FG:0.5KVAC 1min
Safety Standard: EN/UL60950-1,GB4943
EMC Standard: EN55022 Class B,EN61000-4-2,3,4,5,6,8,11 GB17626.5 Level3
Protection:
Over voltage Protection: >115%-135% Rated output voltage
Over load Protection: >105%-150% Auto recovery
Short circuit Protection: Latched
Over Temperature Protection: No
I would like to understand why it's happening, and how to solve it.
Also, I would like to know if it's possible to use Serial without using USB cable? In RealTerm I can choose to listen on an IP address instead of a COM port, but how do I configure my ESP8266 for it ?
Thanks in advance for any help