You might have a point if that was all you had read of scripture. The problem is that these passages in John 6 are referring to the disciples.
John 6
70 Then Jesus replied, Have I not chosen you, the Twelve? Yet one of you is a devil! 71 (He meant Judas, the son of Simon Iscariot, who, though one of the Twelve, was later to betray him.)
Why is this a problem? This doesn't change the meaning of Jesus' words one bit. He had many disciples who were not truly elect. There are many in the church today who don't really believe.
Here's a more complete picture:
Titus 2:11
For the grace of God that bringeth salvation hath appeared to all men.
A better translation of this verse reads: "The grace of God has appeared, bringing salvation for all people..."
This is indeed true. The grace of God is not just for Israel but for people from every nation who call upon the name of the Lord. This verse presents no problem for Calvinism.
John 12:32
And I, when I am lifted up from the earth, will draw all people to myself.
Here's an interesting verse. What does Jesus mean by "all people". In John's writings "all people", "all", and "whole world" usually refers to "people from every nation." Here are some other examples:
1 John 2:2 - He is the propitiation for our sins, and not for ours only but also for the sins of the whole world.
Compare this with John's commentary on Caiaphas' statement:
John 11:49-52 - But one of them, Caiaphas, who was high priest that year, said to them, You know nothing at all. Nor do you understand that it is better for you that one man should die for the people, not that the whole nation should perish. He did not say this of his own accord, but being high priest that year he prophesied that Jesus would die for the nation, and not for the nation only, but also to gather into one the children of God who are scattered abroad.
The language is almost identical. In John's letter he says: "not for us only, but also for the sins of the whole world." In John's gospel he says: "not for the nation only, but also to gather into one the children of God who are scattered abroad."
John, when he says "all", is not usually talking about every single individual, but people from all nations. Therefore the verse you cited does not pose a problem for Calvinism.
1Cor. 15:21-22
For since death came through a human being, the resurrection of the dead has also come through a human being; for as all die in Adam, so all will be made alive in Christ.
All in Adam will die. All in Christ will be made alive. Nothing in here poses a problem for Calvinism.
Rom. 5:18
Therefore just as one mans trespass led to condemnation for all, so one mans act of righteousness leads to justification and life for all.
Same as above. You've got to agree that this only applies to those who are in Christ, otherwise you would believe in universal salvation.
As you can see, Christ has done what is necessary for all men to be saved. Now the ball is in our court. We choose to cooperate with his grace or reject it.
If Christ only made it possible to be saved and salvation depended in any way upon the will of man then no man would be saved.