Just finished Fate/Zero and would love help understanding the end

I watched Fate/Zero for the first time and I don’t understand the ending. Some questions:

How does Kirei get resurrected at the end of Fate Zero and has no heartbeat? Is he undead in Fate Stay Night?

How does Gilgamesh stick around and not have a magic source to keep him there? Whereas Saber gets sent back to wherever heroic spirits are?

What is the deal with the grail being evil?

What does Kotomine discover at the end and then states he has to spend the rest of his life searching for? What is he trying to reach?