I recently took out a pay monthly deal on an iPhone SE and brought my number over from EE. The phone is working perfectly (iMessage included) apart from SMS and MMS messages which always fail to send to any contact. I have full signal and have tried looking online but have not managed to solve the issue.
Sorry to hear of the mobile issues around tests and picture messages. We appreciate you taking the time to make us aware of this via the forum and welcome to the community.
As @newapollo has already mentioned we would make sure the settings are all correct as above. In order to set up MMS you need to send one to yourself after ensuring everything is set as above. Once received you should then be able to send and receive from other contacts.
Please be aware that picture messages (MMS) are chargeable and wherever possible we would recommend using a data based application (ie WhatsApp) to send these as it is a free via those services.