White balance question

I currently shoot a number of pictures in the same lighting situation such as a living room and place my whibal card (or some sort of white or gray card) in one of the pictures. I correct the white balance and then open all the pictures in Adobe Camera Raw and copy the white balance settings to all the pictures.

My question is: Do I have to keep the camera settings the same (i.e. shutter speed, f-stop, ISO settings) for this to work, or can I change the camera settings throughout the shoot (even though the lighting in the room remains the same)?

You can change the settings. It should not have any appreciable impact on WB. The overall exposure is the sum light accumulated via the shutter speed/aperture/ISO combo.