Where did the concept of the soul, after-life, and triune God originate? Some say that the concept of the soul is only mentioned when David tries to stir up his troops before battle, giving them something great to hope for, that Heaven and Hell and scarcely mentioned in the Bible, and lastly that the idea of the Tri-une God is grafted onto Christianity from Philosophy such as that of Aristotle and Plato?? Are these concepts truly Biblical?
You are asking about three different doctrines, and there are, therefore, three different answers. First, let me deal with the concept of progressive revelation. Biblical scholars, both liberal and conservative, recognize that theological and doctrinal ideas are developed gradually, over time, in the scriptures. What is taught about divorce, about how we should treat our neighbors and our enemies, warfare, slavery and many other practical, moral teachings are developed gradually as well. God gave to his people what they were prepared to handle. Specifically with the case of divorce, we can see from Genesis 2 that God intended all along for marriage between one man and one woman, for life, yet God allowed for divorce in the Law of Moses, but as an example of pregressive revelation, he outlawed it for Christians (Matthew 18). This is not because God changed, but because he reveals his will for us in a way which depends on where we are at.
You ask about three doctrines: the nature of the human soul, the nature of the after-life and the trinity. With the soul, I see a rather fully developed idea in the Old Testament already. In Deuteronomy, the Jews were commanded to love the Lord their God with all their soul (Deut 4:29, 6:5 and several other times). The soul is mentioned in Joshua, Judges, 1 Samuel, 1 Kings, 2 Kings… in fifteen of the books. This is a higher percentage of the OT books that the proportion of the NT books which include the word soul. I believe that the concept of the soul is more or less the same throughout the Bible. In fact, the idea of a soul was in existence even in religions outside of Judaism, so this should not be surprising. So, I cannot agree at all with the claim that David made up the soul in order to motivate his troops. This cannot be substantiated.
About the after-life, I believe a pretty good case can be made that this doctrine is an example of progressive revelation. The idea of an afterlife is not absent in the Old Testament, but it is not nearly as significant a topic. Jesus talked about the afterlife, as did Paul, Peter and the other New Testament writers much more than is found in the Old Testament. Daniel 12 gives a very clear description of a future resurrection, heaven and hell, but it is probably the most specific one in the Old Testament. Nevertheless, David and the other psalmists talk about Sheol and Abaddon, which is clearly an after-life idea. In fact, there are dozens of passages in the Old Testament which show that the writer is aware of future judgment and life after death. However, the fact is that this is relatively undeveloped compared to the New Testament. Jesus definitely did not present a new doctrine, but he certainly greatly developed a doctrine which was not nearly so well developed in the Old Testament. In fact, the Pharisees and the Saducees debated over whether there will be a final resurrection. Because the Saducees only used the first five books of the Bible, they were not exposed to as specific a teaching on the afterlife, which will help to explain why they did not believe in the resurrection. In summary on this one, I say that the afterlife is definitely found in the Old Testament, but it is not as well developed a concept and is left more vague in the Old Testament (with the exception of Daniel 12).
Something similar can be said for the trinity/triune nature of God. That Jesus is God is shown by a number of messianic prophecies, including Zechariah 11:12,13 in which God says that he was priced for 30 pieces of silver. We know that "God" in this case is Jesus. Also, there is Isaiah 9:6, which is clearly part of a messianic prophecy, and calls the Messiah (the Son) "Mighty God." There are many passages in the Old Testament which can be used to show that God has a "Son" a "Messiah" who is God. It is harder to prove that the Holy Spirit is God in the Old Testament, but a strong case can be made for this as well. For example, we have the Spirit of God hovering over the waters in Genesis 1:2. David asks God to not take away the Holy Spirit from him in Psalms 51:11. Other passages can be used to show that the Holy Spirit is found in the Old Testament. Bear in mind that God as Father is also not used all that much in the Old Testament. As with the idea of the afterlife, the idea of the trinity is found in the Old Testament, but it is generally not as specific or well developed.
This is the nature of the Scripture. Jesus made more clear the "Mystery" which was hidden for all ages (Ephesians 3:3-9). He completed the revelation and made clear what was not as clear. In summary, I believe that the concept of the human soul is well developed in both the Old and the New Testament. On the contrary, the ideas of the afterlife and the "triune nature" of God are hinted at, suggested, and taught in less clear terms, but these biblical doctrines are completed and stated with more clarity and fullness in the New Testament.
I forgot to deal with the question of whether such ideas were grafted onto the New Testament from Plato or Greek philosophy. I cannot deny the possibility that the vocabulary of the New Testament was at least somewhat influenced by Greek ideas. The language of the New Testament, after all, is Greek. However, I cannot agree that the idea of the soul or the afterlife were taken from Greek ideas, because these ideas preceed Plato and Aristotle in the Bible. As for the trinity, this idea certainly was not taken from Greek philosophy!!!! Definitely not, as this was anathema to the Greeks. Is the trinity idea biblical? Yes, I believe it is. That is another involved discussion, but I will bring this Q & A to a close.