Does the Jewish religion teach predestination, foreordination and election?
Do they teach that David was born in sin?
Do they teach that God hates some people before they were born just because He hated Esau before he was born?
Modern day Judaism is divided into three main sects and several smaller fragments. According to the Wikipedia article "Predestination," modern-day Judaism believes man has a free-will and thus reject the ideas of predestination, foreordination, and election. This also means that they do not accept the concept of total depravity, the idea that people are born into sin.
For all of that, the Old Testament teachings are compatible with those found in the New Testament. The Old Testament teaches very clearly that sin is not inherited. "The soul who sins shall die. The son shall not bear the guilt of the father, nor the father bear the guilt of the son. The righteousness of the righteous shall be upon himself, and the wickedness of the wicked shall be upon himself" (Ezekiel 18:20). The entire chapter of Ezekiel 18 is worth reading as it deals with this topic and it is very easy to understand.
This same chapter also shows that a person's destiny is depended on their actions. God does not want to condemn anyone. ""Do I have any pleasure at all that the wicked should die?" says the Lord GOD, "and not that he should turn from his ways and live?"" (Ezekiel 18:23). Notice that the one making the choice to turn from his sinful ways is the man and not God.
The verse commonly quoted to say David was born in sin is Psalms 51:5, "Behold, I was brought forth in iniquity, and in sin my mother conceived me." Some translations which are strongly influenced by Calvinistic beliefs, such as the New International Version reword this verse to make it appear that David was saying he inherited sin from his mother. However, if you look at the context of the chapter you will find that it was written after David's sin with Bethsheba was exposed. It is a poem of grief over his sin and verse five is David's misery that he was born into a sinful world and its influence on his life lead him into sin. Contrast this with another statement of David when he was in a better mood: "But You are He who took Me out of the womb; You made Me trust while on My mother's breasts. I was cast upon You from birth. From My mother's womb You have been My God" (Psalms 22:9-10). Both in his grief and in his joy, David's comments are completely true. Yet, a Calvinist cannot accept David's statement in Psalms 22 without alteration.
The idea that God hated Esau before birth comes from Malachi 1:2-3: ""I have loved you," says the LORD. "Yet you say, 'In what way have You loved us?' Was not Esau Jacob's brother?" Says the LORD. "Yet Jacob I have loved; but Esau I have hated, and laid waste his mountains and his heritage for the jackals of the wilderness."" Read the verse carefully. Look at its context. Nowhere does it state that Esau was hated before he was born. People assume this because prior to Jacob and Esau's birth, a prophecy was given: "Two nations are in your womb, two peoples shall be separated from your body; one people shall be stronger than the other, and the older shall serve the younger" (Genesis 25:23). Again, read it carefully. Nowhere does it say that the older son is hated or the younger son is loved. God states that the younger son would receive the birthright (the right to be head of the family). Normally the birthright goes to the eldest son, but in this case, God wanted it to go to the youngest. Nothing is stated or implied that the younger would be the better man. As it turns out, Jacob grew up being a God-fearing man while Esau grew up to be an ungodly man. Because of who they became in life, God stated that He loved Jacob and hated Esau.