You shoud call Delta or check their websites for luggage rules including connecting issues.
All those rules are subject to change without notice.
Austin area has a few nice malls. And there is 3 outlet malls nearby.
North of Austin lies Premium Outlet Roundrock.
And in south you have Prime Outlets and Tanger Outlers in San Marcos.
We are specially fond of Prime since it has some high end stores such as Hugo Boss, Zegna, Armani, Lacoste, Ferragamo.
But you do need to drive to those places.