I have used QextSerialPort for many years and am very happy with it. Usually one would build it as a shared library and link your own applications and libraries to it in the usual way (ie edit the LIBS variable in your .pro file).
As for your second question, how you receive the data back is entirely dependent upon what protocol your serial device is using layered on top of the standard RS232 comms protocol. A library like QextSerialPort and the OS take care of the RS232 part but you are responsible for anything above that.
If you can get the bytes of your 128x128 greyscale image then you can create a QImage from them (see the many QImage constructors). You can then use a QLabel (or your own custom widget and QPainter) to show the image.
HTH