A mammogram is uncomfortable...and a bit of an 'out of body' experience. The tech picks up your breast and puts it on a cold metal plate, moves it and manipulates it, positions it, then squeezes the plates, pretty tightly. I would say it is uncomfortable and hurts for a moment. As soon as the compression stops, so does the discomfort. It is very tolerable for the moment, certainly you would not want to hold the position for more than those few seconds.
The medical information and potentially life saving information that a mammogram provides is worth it, hands down. If you've ever had a cavity or any dental work, I would say that you have tolerated similar discomfort. You've given birth, surely that pain is worse than a mammogram.
As for your second question, I have no facts to support this, but I am pretty sure that the mammogram would not pose any health risks. If it did, it would not be the gold standard for early detection.