For privacy purposes, photos won't backup into a cloud unless you have set it to!
No. T-Mobile used to have service called MyAlbum but it was discontinued in 2013 due to prominence of 3rd party providers that specialize in backups such as iCloud and Google Cloud/Photos which are tightly integrated into Android and Apple iOS interface.
As @tmo_lauren stated, these optional services need a cloud account and have to be given permission during the setup process of the device in order to backup personal data such as pics.
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