Are people who have had a heart surgery still expected to have a normal life expectancy or sometimes even longer?

Yes in general: Many people who have heart surgery can resume completely normal lives and activities after recovering from the surgery. The life expectancy of an given individual after heart surgery will depend on what shape they were in before the surgery, the type and extent of surgery and the success of the surgery and any complications.

Depends: There are a lot of heart surgery conditions. Congenital coronary valve pacemaker etc. The coronary patients are most common, and if they do as instructed approach the natural history of their age, sex group. Add smoking, obesity, sedentary, diabetes are additional life impacting situations.