RaspberryPi serial port
I'm quite confident the problem is that the Pi does not have an RS232 interface, while the display has.
The Pi has an (LV-)UART interface, its TX-pin outputs 0V for a logical 0 and 3.3V for a logical 1. This is quite easy to implement, since 3.3V is already available on the Pi. But this only works for communications on a single PCB or within a single device.
For communication between devices over longer distances, a system less prone to interfering signals like RS232 is used. While the logical structure of the waveform (bitrate, timing, start-, stop-, parity- and data-bits) is the same as for UART, the voltage levels are -15V...-3V for a logical 1 and +15V...+3V for a logical 0. This means, there are not only higher (and negative) voltages, their meaning is also inverted.
So, if the display expects RS232 levels and gets that 3.3V levels from the Pi, it mostly doesn't recognize the data, and if it does, it's often just garbage.
And of course, if you connect RX and TX of the same interface, you get what you expect.
But: If the RS232 TX output is not current limited, it could even damage your Pi!
There are UART to RS232 converter boards out there, but if you like to solder, the boards just contain a MAX3232 (plus four capacitors). This IC also generates the higher (and negative) voltage levels from the 3.3V supply voltage from the Pi.
The more common is the MAX232 (guess why it's called so), but it is for 5V, not 3.3V operation.
Finally, because the UART and the RS232 use the same logical structure, it's often not distinguished between both of them, especially by software (programmers). They are often also just called "serial interface", though there are other interfaces like I²C and SPI, which are a type of serial interface, but never considered to be "the" serial interface.
The built-in Raspberry Pi serial port uses voltage levels of 0 to 3.3 Volt, as described here. The USB to serial converter and your display will use RS232 voltage levels of nominally -15V to +15V, with a minimum of -3V/+3V. You need to convert between these two levels.
The port will work when looped back as the output and input voltages are compatible.