A:Answer For the first part of your question- you should receive a discount on your old S9+, as long as it's in working condition and in good shape. How much of a trade in depends on these variables, but I can say that my old S8+ in working order, with no nicks or.scratches netted me $200 towards the S20 Ultra.
As for the 2nd part of your question: yes! Once you bring your phone in and begin the process of registering and setting up your new phone, part of the process will be to transfer your photos, contacts, messages, and apps over to your new phone. This can be a bit of a lengthy process, depending on how much you have on your old phone. To expedite the process, you're best served to backup your photos onto your computer or into the cloud and delete them, as well as any apps you may have on your phone that you no longer use. Some of your apps will continue to download in the background even after you leave with your new phone, but this part of the process took about an hour. And yes, I'm an AT&T customer, as well.
All told, I spent about an hour and a half in store, and some larger apps finished downloading once I was home on my WiFi connection. Good luck on your new phone!