In the in-game dialogue with Vivec, he mentions what happens when he dies in the mortal world:

"Me, I exist at once inside of time and outside of it. It's nice never being dead, too. When I die in the world of time then I'm completely asleep. I'm very much aware that all I have to do is choose to wake. And I'm alive again. Many times I have deliberately tried to wait patiently, a very long, long time before choosing to wake up. And no matter how long it feels like I wait, it always appears, when I wape up, that no time has passed at all."

- Yet I wonder, if this is so, why the Nerevarine is able to murder him in-game, even prior to seperating him from the Heart. Shouldn't Vivec immediately have to get back up on his feet once your character kills him in-game (at least prior to ending the Main Quest)?

- Also, is this power derived solely from Lorkhan's Heart? Or has it something to do with CHIM, making Vivec the sole possixr of this power? In 2920, The Last Year of the First Era, after her battle with Mehrunes Dagon, Almalexia was lying wounded and bleeding in her bed, being tended by healers. This seems to suggest that she was on the verge of dying—like a mortal. And after she woke up:

"Vivec rose with a start, and seeing Almalexia alive and awake, his face broke into a wide grin. He kissed her forehead, and took her hand. At last, there was warmth again in her flesh. Almalexia's peaceful repose suddenly snapped: “Sotha Sil --” “He's alive and well,” replied Vivec. “Working on one of his machines again somewhere."

This in turn seems to imply that Almalexia was initially worried about Sotha Sil's life, like he too, could have died in the fight with Mehrunes Dagon.

So I'm wondering if there is any relevant info on this subject; were the members of the Tribunal truly immortal during their connection with the Heart?

Hm that's a good question, I'm guessing they could die but they would end up being revived sooner or later like Dagoth's servants who were connected to the heart but made notion that they can die but they'll eventually be reborn. So it could be that the Tribunal thought they could die due to at one point being on death's door, the reborn effect could have not be discovered until Dagoth Ur took the heart for his own and began connecting his servants to it. As for Vehk's dialogue in Morrowind it sounds very CHIMmy