Can the Uno handle two serial port functions ?

I still have no picture of how you have wired your project. Is that button control panel only sending data or do you have to send some commands to that panel?

This control panel sends data via a serial port and receives data from the same serial port.
I need to read data and send data to it... Currently, I can only receive data from it...

Do you have a link to the datasheet of that panel?

No, there is not a datasheet available for this as it is a company proprietary piece of equipment.

Not sure why you would need a datasheet for this when the arduino can't pass data on its D1 txd line from the USB regardless if the equipment or anything else is connected to the D1 pin...

Why do you need an Arduino?

Because this device usually interfaces to an old serial type interface and I would like to interface it directly to a USB port on my PC...