Should I take an iron supplement after age fifty and after menopause?

Not necessarily. Some women benefit from iron while menstruating to keep blood count up to counteract menstrual blood loss. Unless you are anemic for other reasons, there is no reason to routinely take iron supplements. This is assuming of course that you eat a well rounded diet with some red meat or green leafy vegetables.
Are you anemic? The main reason to take extra iron would be related to low blood counts (or anemia), or related to a diet low in iron. Given your age of 28, this is probably not something you need to worry about. Perhaps a more important supplement for women of any age group is calcium. I hope this helps!