Can I access all the personal data that my mobile phone operator has accumulated, such as my text messages, and sent and received photos?

No, you cannot access personal data like text messages from your operator. Once they have been deleted from your phone, they are gone. The only information that you can access is your billing information, including the sender’s phone number and the time of transmission. If you have sent or received text messages, and/or photos, it is likely that your mobile operator will keep them on their servers for a period of time that varies amongst operators. They cannot release this information to anyone, even you, without a court order.

See also, Who is involved in delivering content to my mobile phone?