What is the ruling on going out with the Tablighi Jamaat, and how can one reconcile the eternity of the dwellers of Paradise and Hell with Allah being the Last?

There is no contradiction between the eternal abode of the people of Paradise and Hell and Allah being the Last. The permanence of the people of Paradise and Hell is only by Allah's preservation of them. As for Allah, Glorified be He, He is the Last by His very essence. Ibn Ashour indicated that the permanence of anyone other than Allah is not considered, because it is not an essential permanence.