No you cannot send MMS over WiFi. I know with iPhone you can send iMessages which are slightly different than actual messages in some way, not sure how.
Anyway, to the OP you think it's just an issue when sending to AT&T? When you tried to send the same pic to someone else, besides the salesman, was that right then or later after you had left? The reason I ask is because my theory is that there is something about you porting your number that isn't set up correctly. My feeling is that when you are trying to send to AT&T their system is seeing your data coming in with one of their numbers and denying access because the device is unrecognized. So like someone cloned your phone or something and the system is trying to deny unauthorized access. It's been forever ago since I read something similar to this and if I'm not mistaken the poster had to contact AT&T to resolve the issue, or they had their new carrier contact them to ensure that a full release of the number was done or something to that effect. Like I said if it is only to AT&T customers and you are a former customer I think your answer may lie with them. Thinking about it now it seems that the issue was due to the former phone being an iPhone. Which may also explain why you can MMS iPhones on their system.?
One last thing you could try before calling them is a 3rd party app. You are using one of the worst texting apps, besides Hangouts, to text. This isn't Apple the stock apps are not the best integrated apps ever just because they came with the device. I'm just saying.