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Except that Jesus said that he did not come to abolish the Laws (first 5 books of the Bible as you know it) or the Prophets;
"Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. I tell you the truth, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished. Anyone who breaks one of the least of these commandments and teaches others to do the same will be called least in the kingdom of heaven, but whoever practices and teaches these commands will be called great in the kingdom of heaven. For I tell you that unless your righteousness surpasses that of the Pharisees and the teachers of the law, you will certainly not enter the kingdom of heaven."
Following Jesus' advice would not necessarily make the world a better place, then.
Please realise I am Christian, with no background in academic theological studies, though I am actively curious about the very types of questions you are raising.
I will go under flak for this, but you must read the Bible in context. Concerning infanticide; I confess, I did not know of Psalm 137:9, and I also cannot solidly explain this instance, as I find infanticide abhorrent as well. This does not mean that there does not exist an explanation that does not break the foundations of Christianity; it's only that I don't know. My pastor (who has a Theological degree) will know.
I will try and give you other instances for reading the Bible in context. You've quoted the food laws, specifically, the one about seafood (from Leviticus, I forget which chapter though I read it a few days ago). *Modern day* Christians generally believe the reason for the food laws if for hygiene purposes. Eating shell fish is still a common cause for food-poisoning and enteritis even in this day and age..
If a scientist-like mind existed back then, he would have preferred an attempted explanation of pathogens, but God's message was meant to be understood universally, and if not understood (for I'm sure my parents still don't know much at all about infectious disease) then at least followed for their safety and health - see Leviticus' advice on the treatment of infectious diseases, for example, which involved isolation to prevent contamination etc.
The crux of the difference between a myself (a Christian) and yourself (?) is that I believe in the infallibility of the Bible, which is something that can't be proved 100% but only, ultimately, believed in.
(A lot of my information has come from 'The Lion Handbook to the Bible' - I bought it from Amazon; it's very good for answering questions like the one's you've raised.)