Sigh, the ususual Calvinist prooftexts. When does it end?
The passages are interpretted by your
presuppositions rather than the CONTEXT as well as by other Scriptures. Let us take for example, your quotation of Romans 9:18. This out of context quote almost implies that God is abritrary in how He will deal out mercy. It is true that no one can demand that God have mercy on them as the Jews who Paul was addressing were doing. Therefore, God has the right to set the conditions on mercy. Far from being arbitrary, God is willing to give mercy to those who follow His conditions:
Many sorrows shall be to the wicked: but he that trusteth in the LORD, mercy shall compass him about. (Psalm 32:10)
For thou, Lord, art good, and ready to forgive; and plenteous in mercy unto all them that call upon thee. (Psalm 86:5)
So Romans 9:18 is not teaching that God is arbitrary in how He deals out mercy. Neither does He just arbitrarily harden people. Romans 1:24 teaches us that after some time, He gives people up and turns them over to their own lusts. This is what he did with Pharoah. Pharoah first hardened His own heart before God finally assisted in the process.
However, the best response to your Romans 9 prooftexts comes from Romans 9 itself:
But Israel, which followed after the law of righteousness, hath not attained to the law of righteousness. Wherefore? Because they sought it not by faith, but as it were by the works of the law. For they stumbled at that stumblingstone; As it is written, Behold, I lay in Sion a stumblingstone and rock of offence: and whosoever believeth on him shall not be ashamed. (Rom. 9:31-33)
God extends mercy to those who will believe of their own volition. No irresistable grace involved here, no arbitrary mercy extended. God is fair and gives every man equal opportunity to accept or reject His mercy. This passage answers all of your prooftexts and your out of context understanding of them.