Liberty, You pose alot of questions in your post. I will not be able to answer them all here, but will over time I am sure.
The place to start I would quess is the with creation. First, as a scientist, you must agree that science tells us that something can't come from nothing. If you are to exclude the realm of the supernatural, you must agree that creation did not start from nothing. Something had to be there for the big bang to begin. From a scientific standpoint, what was that and how did it get there?
Then, as a scientist, you must agree that you would not place much stock in a theory that could not be replicated or had a strong probability of failure, or depended upon so many unknown factors that it can't be deemed reliable. That is what you have with the portion of evolution or abiogensis that trys to explain the origins of life through evolution. The idea that with just the passage of enough time the elements would come together in such a complex and diverse fashion that all life as we know it would be created is unbelievable. In any other context scientist would say it would never happen. For example, place a watch on a table in pieces. Even a million years later it will still be a watch in pieces. It will not have been put together through the passage of time. What makes you think that all of plant and animal life, much more complicated than a watch would do that?
Biblical archaeology had shown time and again the accuracy of the Bible as an historical text. For example, fairly recent finds in the City of Dan confirm, through the enemies of the Isrealites, that David was a real person and was the King of the Jews. Another example is the story of Joseph being sold in to salvery. It has been noted by a recognized Egyptologist, Kenneth Kitchen from the University of Liverpool that the price noted in Gensis ( twenty silver shekels ) is precisely the going price for slaves in the region during the eighteenth and nineteenth centuries BCE. There are alot more examples of where the stories of the ancient Isralites match with extrabiblical evidence on issues such as inheritence, treaties, oaths, etc.. The importance of this is that it is evidence of the proper settings of the events in the Bible that compare correctly with the time they are believed to have happened, not at when skeptics believe that the Jewish people made them up much later.
Why the Bible and not the other religions you mention? First, the Book of Morman was written by one man a little over one hundred years ago. The events described in the book have yet to be cooberated with one artifact through archeology and instead alot can be traced to Joesph Smith's personal history. The Bible on the other hand was written by numerous authors over thousands of years and has been authenicated over and over again.
Second, the bible is the only holy book that places its spiritual leader ( Jesus) in an historical context with real people and real time. We know when he was born, who sentanced him to death, and when he died. The people who wrote about him stated these things very specifically and could easily have been refuted to obscurity. The other stories of ancient Gods, are not so specific, instead, they talk about things that happened in ancient history with no historical context. Also, the Bible is the only holy book that makes specific prophecies that have come true.
Finally, what makes you think God has not made himself known? Do you want him to appear in the sky and annouce to each person he is there? If so, where would faith come in? In truth, God has presented himself everywhere. He is the intelligent designer in creation, he is the divine author behind the Bible, He is the real man Jesus who came to earth, he is the one who spoke through prophets and whose prophecies came true.
I know this is only a start to our conversation. But I want to aske you a question. Do you expect to prove the basis of faith through science based upon our limited abilites to understand the world around us? For example, do you dismiss that Jesus could have risen from the dead because we cannot explain that scientifically?