Q1 - If I want to receive serial comms from another device via coming in on PIN 0 (serial receive) does the the USB connection from the board to my PC have to be disconnected?
No you don't have to disconnect it, however what you have to do is make sure you don't send serial data from the PC to the Arduino USB serial port as the data would clash and garble with the external serial data you have wired going to pin 0.
Q2- If yes, then how could I monitor the incoming serial via the Arduino IDE's serial monitor?
Again no. And the serial hardware and software on the Arduino allows for independent full duplex communications, so you can still have serial output commands in your Arduino sketch and the data will show up in the PC serial monitor's receive window.
Another more common solution is to use one of the Arduino serial software libraries to handle the external serial receive data (to any pin) and leave pins 0 and 1 as is for PC use. You could then have code in your program to send anything received from the software serial to the normal hardware serial so it can be monitored on the PC
PS: you might want to read the user feedback comments on those RF modules, they can be quite tricky to get working reliably. http://www.sparkfun.com/commerce/product_info.php?products_id=8946