Update:
I swapped my NodeMCU for an ARduino Mega board (from a starter kit).
Serial works like a charm... no bugs at all after deep sleep.
Hence problem solved. 
Seems that the NodeMCU USB-Serial does not handle well if your board goes into deep sleep.
(note: I also have much less gibberish I expereinced sometimes in my logs. With the arduino, all serial output is clean/clear).