It is not a sentence (because it has no subject and verb), just a subordinate phrase. The phrase says nothing about doing anything because it is not a sentence and contains no verb to perform any action. The whole thing is just one big long noun phrase based on the noun "faith". "To be together" is an adjective phrase that modifies "commitment". If you eliminate that adjective phrase the meaning of the sentence remains the same except that you no longer know what kind of commitment it is: "shared faith that members' needs will be met through commitment"

No, not necessarily 'doing everything together'. 'Be together' could mean a lot of things - you can't really tell from this sentence. The most logical conclusion would be that they can continue to be members of whatever group 'members' refers to.