1. Sauron's the only concrete example we have of a multiple shape-shifter amongst the Maiar. There are examples of other Maiar shifting between spirit (fëa) and physical (hröa) form in Valinor - Olórin, for instance - but not the sheer diversity of forms adopted by Sauron. Contra, the Balrogs remain Balrogs throughout the Wars of Beleriand, indeed since their original Rebellion against Eru. Tolkien also explored the idea of Huan and the great eagles being Maiar in permanent physical form.
2. Regarding 'death', in the 'Myths Transformed' collection of Tolkien's essays, there seem to have been different rules for those Maiar who had rebelled. The 'death' of their incarnate forms had a greater consequence - damnation, "ie. reduced to impotence, infinitely recessive: still hating but unable more and more to make it effective physically...". That covers the Balrogs and, at least as far as the First Age is concerned, Sauron too. At the resolution of the duel between Sauron and Huan, Lúthien points out to Sauron that if he allows his current body to die, he would be "everlastingly... naked" - ie. unable to reconstruct himself in the physical world. The fact that Gothmog, mightiest of the Balrogs, isn't listed as present at the final battle of the War of Wrath implies that his 'death' at the hands of Ecthelion was permanent. Olórin, on the other hand, was still in a 'state of grace' when his Gandalf form was destroyed, and was able / allowed / empowered to adopt a new hröa in Middle-earth.
3. In my view, the One Ring changes the above rules, so making Sauron a true exception. He imbues the One Ring with so much of his own power that his physical destruction (on Númenor; and then at the hands of Gil-galad, Elendil and Isildur) is no longer enough to end his effective existence in Arda. The One Ring itself has enough of Sauron's essence in it that it serves as a link to his reincorporation as a physical entity. Thus the whole point of the Quest for Mount Doom - the One Ring must be destroyed if Sauron is ever to be removed permanently from the equation. Prior to the forging of the One Ring, however, Sauron could be reduced to permanent 'impotence', as Tolkien put it - as demonstrated by his fear of 'death' at the hands (jaws, paws??) of Huan. You mention Númenor but I think this is actually an example of the new rule in action for the first time - Sauron can rebuild a new (albeit degraded) form precisely because of the existence of the One Ring.

‘Thither I came at last, to the uttermost foundations of stone. He was with me still. His fire was quenched, but now he was a thing of slime, stronger than a strangling snake.
‘We fought far under the living earth, where time is not counted. Ever he clutched me, and ever I hewed him, till at last he fled into dark tunnels. They were not made by Durin’s folk, Gimli son of Glóin. Far, far below the deepest delving of the Dwarves, the world is gnawed by nameless things. Even Sauron knows them not. They are older than he. Now I have walked there, but I will bring no report to darken the light of day. In that despair my enemy was my only hope, and I pursued him, clutching at his heel. Thus he brought me back at last to the secret ways of Khazad-dûm: too well he knew them all. Ever up now we went, until we came to the Endless Stair.’
‘Long has that been lost,’ said Gimli. ‘Many have said that it was never made save in legend, but others say that it was destroyed.’
‘It was made, and it had not been destroyed,’ said Gandalf. ‘From the lowest dungeon to the highest peak it climbed, ascending in unbroken spiral in many thousand steps, until it issued at last in Durin’s Tower carved in the living rock of Zirak-zigil, the pinnacle of the Silvertine. ‘There upon Celebdil was a lonely window in the snow, and before it lay a narrow space, a dizzy eyrie above the mists of the world. The sun shone fiercely there, but all below was wrapped in cloud. Out he sprang, and even as I came behind, he burst into new flame. There was none to see, or perhaps in after ages songs would still be sung of the Battle of the Peak.’ Suddenly Gandalf laughed. ‘But what would they say in song? Those that looked up from afar thought that the mountain was crowned with storm. Thunder they heard, and lightning, they said, smote upon Celebdil, and leaped back broken into tongues of fire. Is not that enough? A great smoke rose about us, vapour and steam. Ice fell like rain. I threw down my enemy, and he fell from the high place and broke the mountain-side where he smote it in his ruin.’ (LotR, III.5, underlines by squire)

Suddenly Gandalf laughed. ‘But what would they say in song? Those that looked up from afar thought that the mountain was crowned with storm. Thunder they heard, and lightning, they said, smote upon Celebdil, and leaped back broken into tongues of fire. Is not that enough? A great smoke rose about us, vapour and steam...'