Is it necessary to mention all of the opening supplications (Du'as Al-Istiftah) narrated from the Prophet, peace and blessings be upon him, in every prayer, or is it sufficient to mention only one formula?

The opening supplication (Du'a al-Istiftah) is sunnah according to the majority of scholars. There are multiple forms of it established in the Sunnah. Whoever recites one of these forms has fulfilled the sunnah and is not required to recite all the reported forms.