Is it permissible to supplicate before the taslim in prayer or after the tashahhud, and should one say before it: "All praise is due to Allah, Lord of the Worlds, and peace and blessings be upon the noblest of messengers, our master Muhammad"?

Supplicating after the tashahhud and before the taslim is recommended according to the majority of scholars. It has not been authentically reported from the Prophet (peace be upon him) nor the Salaf (pious predecessors) to begin this supplication with praise (hamd) and prayers upon the Messenger. It is recommended to say: "I seek refuge with Allah from the punishment of Hellfire, and from the punishment of the grave, and from the trial of life and death, and from the trial of the Antichrist (Al-Masih Ad-Dajjal)," as narrated in the hadith of Abu Hurairah. There is no harm in supplicating with what has been reported in the Qur’an, or the Sunnah, or from the Companions and the righteous Salaf.