I try to send a picture as a text but it won't send.
I don't know but I had the same problem. I was able to send and download pictures from a text by turning data on even though I have a WiFi only plan with ATT.
Under Settings->Mobile networks I checked "Data enabled" and it worked. I was connected to WiFi. I haven't tried when not connected to WiFi. I also plan to keep this unchecked unless I need it as I don't have a data plan. Didn't get charged for any data.