I am a breastfeeding mother, and I will be flying this weekend. My first question is, will there be a place for me to pump my milk during my layover? My second question, can I store my breastmilk in a cooler that isn't my carry-on or personal item?

At DFW there s not such a place.

I honestly havent seen a designated place maybe a lounge or bathrooms. You could always bring a small cooler as a "carry on" item and put it under the plane upon boarding your plane (after security). They usually call it on the intercom for checking bags under the plane. You can bring other liquids/drinks on the plane that you purchase after you go through security. Just bring a small cooler and you should be good.