Leviticus: The description of ritual laws for Israelite religion.

1. Why don't Christians abide by these laws today? (They consider everything in the Bible to be God's word, therefore are not his biblical commandments valid?)

The Law of Moses revolved around the Levitical, or Aaronic Priesthood. Some of the practices were symbollic of the mission and life of the Messiah, ie sacrifices = God sacrificing his son. Jesus was a fulfillment of the law, so the similitudinous rituals were no longer necessary. Sacrifices were replaced by the Sacrament. Matthew 5:17 "Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil." The other reason is because the Melchezidek Priesthood, which Jesus reinstated, takes authority over the Levitical Priesthood. Hebrews 7:11-12, "If therefore perfection were by the Levitical priesthood, (for under it the people received the law,) what further need was there that another priest should rise after the order of Melchisedec, and not be called after the order of Aaron? For the priesthood being changed, there is made of necessity a change also of the law." Old things have passed away, and things are new.

2. Isn't a bit strange that the Jewish writers of the bible proclaimed that Jews are God's chosen people and then proclaimed that this is God's Holy Word?

"Well, it's like Yogi Bera used to say, "It ain't bragging if you can do it." The Book of Mormon also testified that the Jews were the covenant people. In a revelation given to Nephi, God says, "O ye Gentiles, have ye remembered the Jews, mine ancient covenant people?" (2 Nephi 29:5) But of course, the people in the Book of Mormon were also of the Tribe of Israel, but this gives two different accounts from two different testaments about the Jews status in Biblical Times. So no, it's not strange at all.

3. Why is it that all 4 gospels (Matthew, Mark, Luke and John) have diferent versions and contradictions of what happened after Jesus' death? Shouldn't the "inerrant" word of God be more accurate?

I didn't read any critical contradictions that would alter the integrity of the different people's accounts. In each account, Jesus appeared at the tomb to Mary Magdalene. He appeared to His Apostles, He commanded them to preach the gospel, and He ascended into Heaven. Whether or not someone recollected the other Mary being at the tomb, or Jesus appearing to disciples along the road doesn't discredit the other accounts. Different people recollect and saw different things. And, since the gospels were written years after the Crucifixion, and some were dictated accounts, it is a testimony to their divine nature that they do tell the same accounts, differing only in personal accounts and details. It is also possible that when they were originally penned, the details meticulously matched but were altered through different translations. In any case, the Book of Mormon provides another witness that Jesus was crucified, He was resurrected, and that the biblical accounts are accurate.