Think how women feel who have male ob/gyns putting their fingers up inside their vaginas. The doctors have seen it all before, but that doesn't mean the patient has.
Hard to say. I've had my penis looked at during a physical and the doctor (also an older woman) took about 15 seconds. It's possible she was being thorough, but if you don't think she was you should say something. I've heard that doctors will wait for erections to go down. Normally they also have someone supervise in case of sexual harassment.
That is a good thread. I've been also wondering how situations like this should be treated. There's a thin line between proffesionalism and sexualy inducing behavior.
From what it sounds like, she was checking for signs of tumors, cancer, and hernias all at the same time. You've got yourself a good doctor.