Why is the Islamic version concerning Talut and Jalut not consistent with the Biblical version? Do Muslims have another source of this story besides the Bible?
By the nature of oral literature, when a story is told, it is often altered or embellished, and this is not considered a problem in cultures that transmit their literature and history orally. The oral retelling of historical events still continues in many parts of Africa, almost as a spiritual ritual. The genealogist, or story-teller, will claim to have heard the story from his father, who heard it from his father, and so on. There is meant to be a chain of transmission which should protect against error; nevertheless, while you can find the same basic framework of the narrative in different accounts, there will often be notable differences.
The narratives of the Bible were compiled over time by different groups of scribes. Initially, narratives from the Bible were transmitted orally - even for several generations. Eventually they came to be written down. The accounts that have been written in the Bible may not be the only accounts that exist of certain narratives. There may be several variations.
In fact, often certain points that the Qur'an makes about particular doctrines held among Jews or Christians actually refer to apocryphal beliefs that were not held by the majority. There were often sects and sub-sects in Arabia and Iraq and not much has been written about them.