/dev:
Experiment #1 looks like you are testing simultaneous sending and receiving. You could call that "full duplex"
Yes, that's right, I misspoke, sorry.
/dev:
Try changing line 234 in NeoSWSerial.cpp from this:char c = rxBuffer[rxTail];...to this:
uint8_t c = rxBuffer[rxTail];
That's exactly what I did. Now receiving data coincides with the SoftwareSerial library.
But the main program still does not work ... I do not understand anything. 
Thanks,
Marat