Welcome to the Community Forum! You have come to the right place to receive a resolution to this issue. I would be delighted to help out!
Group messages and pictures messages both require cellular data in order to be sent and received. Since the $30 GoPhone plan does not include a data allowance, this would be why you are unable to send these types of messages.
You can purchase bolt on data in the amount of 250MB for $5, or you can switch your plan to the $45/monthly plan with 6GB of data, or the $65/monthly plan with unlimited data. Just log into your GoPhone account to make the switch!
I hope you found this informative! Have a wonderful day!
Portia, AT&T Community Specialist
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