"God desires all men to be saved" from a Calvinist perspective? If I understand correctly, Calvinists believe that God selects certain people for salvation based solely on His will... that is, the selection has nothing to do with the people themselves.
My question is about the following passages:

This is good and acceptable in the sight of God our Savior, who desires all men to be saved and to come to the knowledge of the truth.  1 Timothy 2:3-4
The Lord is not slow about His promise, as some count slowness, but is patient toward you, not wishing for any to perish but for all to come to repentance.  2 Peter 3:9
Again, when a wicked man turns away from his wickedness which he has committed and practices justice and righteousness, he will save his life. Because he considered and turned away from all his transgressions which he had committed, he shall surely live; he shall not die. . . . For I have no pleasure in the death of anyone who dies,” declares the Lord God. “Therefore, repent and live.” Ezekiel 18:27-32

It seems ... like God wants everyone to be saved and &quot;live&quot;, and does not want people to die and go to Hell.  If this is the will of God, and God decides who will be saved based solely on His will ... then why isn't everyone going to be saved?
To be fair to Calvin, why not go straight to the horses mouth. Calvin did not believe this kind of verse (1 Tim 2:3) implied God's desire to save every man. Here is where we discover limited atonement as proposed by Calvin and is various different ways supported by the most eminent Calvinists that have ever lived, including in my mind one of the greatest theologians ever, John Owen. (I disagree with these men that I admire but have some support in Luther, so the balance is even).


  In short, as the calling is a proof of the secret election, so they whom God makes partakers of his gospel are admitted by him to possess salvation; because the gospel reveals to us the righteousness of God, which is a sure entrance into life. Hence we see the childish folly of those who represent this passage to be opposed to predestination. "If God" say they, "wishes all men indiscriminately to be saved, it is false that some are predestined by his eternal purpose to salvation, and others to perdition." They might have had some ground for saying this, if Paul were speaking here about individual men; although even then we should not have wanted the means of replying to their argument; for, although the: will of God ought not to be judged from his secret decrees, when he reveals them to us by outward signs, yet it does not therefore follow that he has not determined with himself what he intends to do as to every individual man. But I say nothing on that subject, because it has nothing to do with this passage; for the Apostle simply means, that there is no people and no rank in the world that is excluded from salvation; because God wishes that the gospel should be proclaimed to all without exception. Now the preaching of the gospel gives life; and hence he justly concludes that God invites all equally to partake salvation. But the present discourse relates to classes of men, and not to individual persons; for his sole object is, to include in this number princes and foreign nations. (John Calvin's Commentary 1 Timothy)


Even Luther took this approach before Calvin regarding this specific verse:


  “God desires all men to be saved” (1 Tim. 2:4), and He gave His Son for us men and created man for eternal life. Likewise: All things exist for man, and he himself exists for God that he may enjoy Him, etc.39 These points and others like them can be refuted as easily as the first one. For these verses must always be understood as pertaining to the elect only, as the apostle says in 2 Tim. 2:10 “everything for the sake of the elect.” For in an absolute sense Christ did not die for all, because He says: “This is My blood which is poured out for you” and “for many”—He does not say: for all—“for the forgiveness of sins” (Mark 14:24, Matt 26:28) 
  (Luther's Works Volume 25.376)


As a 90-95% Calvinist (If I was a 100% anything this might constitute idolatry!) I am persuaded to agree with Luther and Calvin with respect to these particular verses but at the same time believe that God does love all men beyond the elect and that how this pertains to free will is not as cut and dry as Calvin thought. Luther also used  1 Tim 2:4 to argue about God's general care for all mankind in a separate Volume. 

See this post arguing against limited atonement

What is the Biblical argument against Limited Atonement?

I also do not think it was so cut and dry in Luther's mind, see here an argument for God even loving those 'predestined to damnation'.

Does God hate unborn children?

Strictly speaking as a Calvinists I depart from Calvin on this one point. I consider it Calvin's point of weakness and failure. So do many others who deeply identify with Calvinistic theology and who are comfortable being called by that label.