Does the Pro Mini support using the SoftwareSerial library? If so, are there any restrictions on which pins to use?
The hardware (at least the heart / the micro at it's heart) of the Pro Mini is the same as the Uno. So yes, it works (the same as an Uno).
Ok, thanks... one additional question. If I use the console cable (connect to the 6-pin header) and I have a device connected to Rx and Tx (the source of the serial stream). Can I use the IDE Serial Monitor to view the serial communications between the Mini and external device?
When the serial-usb cable is connected you cannot monitor the communication. Mainly, because the serial cable will block the communication from the external device (the TX pin of the external device and the serial-usb are paralleled. If you would disconnect the TX from the serial cable you are able to see what the external device transmits.
If you fully want to monitor it, use two usb-serial cables (and two terminals/Serial monitors) to see all. Connect RX of one cable to RX, RX of the other cable to TX and connect one GND of one of the cables to GND if you don't power it from that PC. (You could also connect Vcc o power it from the PC.) That way you have one terminal with what the Arduino says to the external device and one terminal with what the external device says to the Arduino.
Ok, that information was most helpful.
I'm using the 2nd serial-USB cable to connect to 2 pins on the Mini which I've setup using SoftwareSerial. I'm sending debug info to that connection so I can monitor the sketch execution. Based on your last post, if I use the console serial-USB cable and using breadboard wires, connect the RX to the RX on the Mini and the GND. Would that allow me to monitor the incoming serial stream to the Mini (I don't need to monitor the Mini's output so the hardware serial)?
You might need to connect.
USB Serial RX -> Pro mini SoftwareSerial TX
USB Serial TX -> Pro mini SoftwareSerial RX
GND -> GND
I tried the above setup with Hardware serial. I used coolterm to monitor the serial communication.
I wasn't clear in my previous post... I've successfully monitored the SoftwareSerial RX/TX...
The problem I'm now trying to solve is being able to monitor the incoming serial stream on the Mini's RX/TX labeled pins (hardware serial connection). Based on septillion's post, I was confirming that if I connect a 2nd serial-usb connection to RX and GND, I will be able to monitor the incoming serial stream.
I think you should be able to see the communication if you connect Tx of pro mini to Rx of USB Serial and GND. Are you facing any issues in the setup?
But he wants to monitor the data from the external device. To do so, simply connect
Pro Mini RX(=external device TX) -> USB Serial RX
If you power the Pro Mini from the PC (via another cable) you don't even need to connect GND's 
septillion:
But he wants to monitor the data from the external device. To do so, simply connectPro Mini RX(=external device TX) -> USB Serial RX
Sorry I misunderstood the requirement.
In my testing what I normally do is mirror what ever reads from Software serial to Hardware serial. This way I can monitor the communication via IDE's Serial monitor and no need to check individual Software Serial Rx (I have multiple software serial). Not sure whether you can use this option.