Does Sundance Square have an independent book store that sells postcards?

An independent (aka local) bookstore near Sundance Square is the Backdoor Book Shop at W 8th & Throckmorton, around the corner from Hyde Park, next to J's Burgers. They have a wife book selection but aren't likely to have much in postcards. A not-so independent alternative is the TCC Trinity River campus bookstore at 300 Trinity Campus Circle. It's more likely to have postcards, though perhaps not unusual options an indie store might have.

There is a souvenir shop by the seating area, there was a Barnes and noble, but that's gone.

I think they used to. I have only been there once

No they do not

Nope.

Barnes and Noble