[Zigûr]

1. What caused Sauron to become evil? In the narrowest sense, the influence of Melkor (of course). More broadly, his perfectionist desire for Arda to be ordered and completed according to design, which attracted him to the service of Melkor, and his impatience for this situation to come about.

"it had been his virtue (and therefore also the cause of his fall, and of his relapse) that he loved order and coordination, and disliked all confusion and wasteful friction. (It was the apparent will and power of Melkor to effect his designs quickly and masterfully that had first attracted Sauron to him.)" ["Notes on Motives in the Silmarillion" in 'Morgoth's Ring']

2. Middle-earth under the absolute domination of Sauron would have been a world without freedom, of slavery and misery as punishment for all creatures in the West that had defied his will for so long. In Rhûn and Harad he was already held in dread and reverence as a god. Consider the following:

Gandalf to Frodo: "hobbits as miserable slaves would please him far more than hobbits happy and free. There is such a thing as malice and revenge." ["The Shadow of the Past"]

The Mouth of Sauron: "All lands east of the Anduin shall be Sauron's for ever, solely" while in the West the Mouth himself "would be their tyrant and they his slaves." ["The Black Gate Opens"]

The words of Professor Tolkien personally: "Sauron desired to be a God-King, and was held to be this by his servants; if he had been victorious he would have demanded divine honour from all rational creatures and absolute temporal power over the whole world." [Letter 183]

3. Like all evil beings I believe Sauron experienced fear acutely: fear of failure, fear of personal injury and fear that mastery of the One Ring would be seized by another being. As is quoted above he felt admiration for Morgoth until his defeat, but afterwards I would argue that he had no love for any being other than himself. He experienced frustration, hatred, the lust for power, and satisfaction, even pleasure, in triumph over his enemies, the domination of others and the fulfillment of his will. His sadistic enjoyment of the suffering of others can be observed in The Silmarillion, particularly in his treatment of Gorlim. In Akallabêth a noteworthy instance of his arrogance is his when he laughs three times about the folly of Ar-Pharazôn and the destruction of the Númenoréans.

I'm not sure how long Sauron dwelled in the West - up until recently I had believed (incorrectly) that he had abandoned the society of the Valar after the fall of Almaren, but he must have left before the Battle of the Powers because he was in command of Angband at that time. He was, however, able to convince Celebrimbor and the Gwaith-i-Mírdain that he was an emissary of the Valar during the Second Age, so he must have had a decent enough memory of how they behaved.

Regarding the Music we are afforded further information in "Notes on Motives in the Silmarillion", which really is the essential and definitive text for understanding Sauron: "Sauron could not, of course, be a 'sincere' atheist. Though one of the minor spirit created before the world, he knew Eru, according to his measure. He probably deluded himself with the notion that the Valar (including Melkor) having failed, Eru had simply abandoned Eä, or at any rate Arda, and would not concern himself with it anymore." He also "regarded the motives of Manwë as precisely the same as his own" regarding Saruman, so he must have given some serious thought to the Valar as late as the Third Age.

I could go on but this post would get seriously out of control. I can't praise Morgoth's Ring enough as a source of invaluable information for understanding Sauron, his personality and his motives. I am absolutely fascinated by Sauron as a character (rather morbidly) and find those Notes to be an excellent resource.