Traditionally it was more about bringing some food, but there is quite a gift industry centered around Thanksgiving these days. Even so, they are mostly food related - you can see some examples here.
Do people give gifts at Thanksgiving?
Depends to show honor you don't to because usually Thanksgiving is like a great meal enjoying it being single or sharing with the people you care
You,people give gifts at Thanksgiving.
You, they do offer gifts.
For me it depends upon the situation I say so because when that's your family doing in every thanks giving party it's nice....