Thank you very much for the advice and assistance, @/dev! I am very grateful.
/dev:
"Does not work" is ambiguous. What do you mean, specifically?
I tried to use the library SoftwareSerial: when testing full-duplex packets are lost, but the whole package seemed so {101030255255255} and button worked on the display.
Your library NeoSWSerial: packages arrive safely, also {101030255255255}, but on the screen no action is happening. It breaks my brain.
/dev:
Use Serial for the Nextion
I already wrote that I used the Serial. 
The result is the same as with the SoftwareSerial: touch screen works, but I need to press until I get the whole package.
Besides, I need a Serial for connecting to a computer. I take readings from the load cell and plotted. I even have ftdi232 converter, I am ready to change everything, but it does not help.
I tried to test NeoSWSerial in two ways:
- Direct on the protocol. Everything worked well.
- Using Nextion library. The display does not work, but the packages were. I think if I look at why not joined the library, it will work as it should. I can not any more than anything other to suggest ...
Thanks,
Marat