How can I rotate the camera around my character with my weapon out?
Solution 1:
Hold F (for me it's actually V (same key I use to switch between 1st and 3rd person views), not sure if I remapped something or not) or middle mouse while you move the mouse around.
If you're using a gamepad then you should hold the button that puts the camera into 3rd person mode, and then rotate the camera around your character. For example X-Box 360 gamepad this would be the Back button.