How does surgery affect people who have stage 3 rectal cancer?

Depends. On where in the rectum the tumor is and what specific surgery is performed, I need more information to adequately answer this question.
Hard to say. Some people are cured and some are not. You can't predict who will be in each catergory. My dad had stage 3. Best chance for survival at that time was 5% for 5 years. He lived 25 years after surgeryand died at age 95. Go figure. All is not lost with the diagnosis of cancer.