Can the Uno handle two serial port functions ?

I will try the SoftwareSerial library which should allow me to use pins (other than 0 & 1) because I am concerned about communication issues if pin 0 & 1 are shared for both my serial device and the USB to the PC unless I can see some example code that works...

What do you want to do? If you want your UNO to be a USB2Serial device you can just connect it via USB to your PC and connect the TTL serial device to pins 0 and 1. Voilà, you have your USB2Serial. You don't need any software to be run on the UNO, it acts as a USB2Serial converter.
If you need something else than a USB2Serial converter, tell us what you want to achieve!

The SoftwareSerial class works OK for baud rates up to 9600, with some devices even up to 38400. I personally never got beyond that limit.