Can I buy a gift card at customer service

Yes

Food court

Yes they have gift cards

I saw advertisement for gift cards therefore I'm sure they do. However, I did not see the actual place where you could get them.

Yes you can at a specific location they have gift cards

When I went there during Tax Free weekend, I noticed in the Food Court area a bunch of Gift Cards. Not 100% on which ones they were, but I did see them.

I believe so but not absolutely certain.