I tried to replace the 19 line from
SoftwareSerial nexSerial(2, 3); // RX, TX
to
#define nexSerial Serial
and connect Rx/Tx from display to pins 0 and 1 on Arduino UNO.
The problem is the same. Apparently, hardware port half-duplex too. 
I tried to replace the 19 line from
SoftwareSerial nexSerial(2, 3); // RX, TX
to
#define nexSerial Serial
and connect Rx/Tx from display to pins 0 and 1 on Arduino UNO.
The problem is the same. Apparently, hardware port half-duplex too.