After the end of morrowind azura says that Vivec still lives.What happened to him in the next years?Is he dead or alive?

How can a god truly die?

I didn't understand what you actually mean

What happened to Vivec depends entirely on your actions in Morrowind until another game retcons his fate out of the hands of players. If you killed him, he is dead. If you spared him, like the petty dike he was, he wilfully allowed a giant meteorite to crash into his city, causing the worst disaster in Dunmer history and then slinked off into obscurity, probably to go back to polishing Molag Bal's spear.

No, sorry. If you killed Him, His mortal body is dead. If you spared Him, the loss of the Heart of Lorkhan sufficiently diminished His powers to break the spell He used to prevent the giant meteorite from crashing into His city; presumably this was that petty [censored] Azura's plan all along (her 'revenge' on the Dunmer people for replacing her with better Gods).

As for Molag Bal, the 36 Lessons of Vivec, Lesson 14, says: "But Vivec had made of his spear a more terrible thing, from a secret he had bitten off from the King of [censored]. And so he sent Molag Bal tumbling into the crack of the Biters and swore forever that he would not deem the King beautiful ever again".

If you accept MK's possibilities as scripture, http://c0da.es/t/c0da.

"When Nerevar returned, he saw the frozen comet above his lord's city. He asked whether or not Vivec wanted it removed. 'I would have done so myself if I wanted, silly Hortator. I shall keep it there with its last intention intact, so that if the love of the people of this city for me ever disappear, so shall the power that holds back their destruction.' Nerevar said, 'Love is under your will only.' Vivec smiled and told the Hortator that he had become a Minister of Truth." - Sermon 33

He set that up. He could have removed it, but he chose to leave it there. The destruction it caused was collateral damage that he created for the people of Morrowind who had no choice in the matters, caused by Azura's vendetta against the Tribunal, whose ambitions of benevolent godhood were doomed anyway since Dagoth Ur thought of it first. Unless that is, Azura set up Dagoth Ur to succeed over the Tribunal, so that they all had to lose the Heart. Plus it was neither him nor Azura who sent the moon there.

Based on Sermon 14, I wouldn't expect him to be back with Molag Bal, but then it wouldn't the first oath he broke.

Yes, his mortal body would be dead. Ergo, he is dead. His soul may yet persist, just like that of any other mortal, but if the Nerevarine chose it, he died a violent death just like anyone else who crossed the Nerevarine on their path to greatness. I like to think that the Tribunal unwittingly bound themselves to the spheres of the respective Daedra who they claimed were their anticipations. It would be a satisfying karmic twist to reward their hubris. So, Sotha Sil would be bound to Moonshadow, Almalexia to Boethiah's Realm and Vivec to Spiral Skein. Vivec might not consider that much of a punishment though, considering his penchant for six and murder.

I think you're projecting on Azura. All we can do is speculate on what she wanted in the wake of the downfall of the Tribunal. We can't say for sure that she would have wanted Lie Rock to come crashing down. But, we do know that Vivec definitely wanted to use Lie Rock as a fail-safe against the people's rejection. Either they would love him eternally or he would let the meteorite resume its collision course and reek havoc on the people of his namesake city and the rest of Morrowind. And because the institution of the Tribunal was undone and the people started to doubt Vivec and his peers, he let Lie Rock fall and brought on the Red Year.

Yes because it's totally better to let Dagoth Ur complete his plan and end up taking over all of creation and let him set himself up as the dreamer. Nope, what Azura did was bad and we should hate her for it whereas letting the heart and Dagoth Ur remain was the good thing to do!

My god, the lengths people go to to do their petty Azura hate straw grasping to make her look bad. Azura had literally nothing to do with the Red Year or wanted revenge on the Dunmer. Hell, she didn't even tell Sul to break the machine that kept the Ministry of Truth up, that was all Sul. Actually bother to do your research before spouting out inaccurate information.

Also if Azura wanted 'revenge' why did she have her priests guide refugees out of Morrowind as Red Mountain erupted? Actually think before spreading this nonsense.

This.

It's true, Azura is not "good"--she's a Daedra. But compared to other Daedra, she seems quite nice, and there's precious little evidence to paint her as evil. The people she's chosen as her own--the Dunmer (who, it's worth recalling, do not regard their transfiguration as a curse) and the Khajiit--certainly don't think her so. Without her intervention, all of Tamriel would be infected with corprus and Dagoth Ur, well-intentioned or not, would doom the world.

As for the Tribunal, my opinions of them vacillate. Or at least of Vivec--Almalexia is completely and utterly mad. They did evil to presume to claim godhood, but they also did some good with their powers. And I'd like to believe that Vivec spoke the truth when he said he regretted it. And yet nevertheless the source of the power was still corrupt. From a narrative perspective, it's a perfect situation: the Tribunal uses evil power with questionable motives to do good while Dagoth Ur uses evil power with good intentions to do evil--no one is innocent yet no one is entirely guilty either. One of the many layers of ambiguity that makes Morrowind so special.