Can I take a picture with my Ipad 4 of the person I am fact timing with?
No - unless a screenshot works with FaceTime and I have never tried that myself. But to take a photo - no.
You can take a screen shot.
Simultaneously press the on / off switch and the center home button. You will notice an on-screen flash. If you have sound enabled, you will hear a camera click.
Retrieving data ...