Origin of Indian philosophy

It is always a profound learning experience meeting my partner Raghoo Sinha. Recently, we were discussing how and why agnosticism is one of the six major schools of Indian philosophy. Some of  my learning is as follows:

1. One of the first appreciations was that there is an exorable Law of Karma, which is Newtonian in nature. We will have to pay for our actions or inactions, and there is no escape. 
2. Yet, in real life it was seen often enough that those who do good suffer and those who have bad karma enjoy. In an effort to reconcile this contradiction, concept of multiple births was propounded. It was surmised that one not only reaps the fruits of present-life karmas but also previous lives' karmas that have not been 'redeemed'. 
3. Unredeemed karmas also get shaped as 'samskaras'.
4. Now, who will ensure proper record of these karmas and transfer of these records from one birth to the other? Thus, came the construct of 'indestructible' atma which carries on. It is to be noted that the concept of atma was propounded much before the concept of 'brahmatma' came in.
5. What happens when one day, all the karmas are redeemed and balance is neither positive nor negative? This is called 'moksha' and the cycle of births and deaths is no longer necessary. If this were so, what will happen to atma, which was the vehicle of continuity? Here 'brahmatma' was brought in and atma is suposed to get merged with brahmatma. 

In ancient philosophy, the concept of inexorability of karmas was so strong that no propitiation of gods could save one from bearing the fruits of one's karmas. This later got diluted in vedas and more so in bhakti period. Influence of western thought processes and religions also played a role in cultivation of benign God or gods who could be 'won over' through bhakti and one could 'wash away' one's sins through worship or a holy dip or such 'remedies'. Some gods could also turn vindictive suitably punish the non-believers!!  Birth and perpetuation of 'priests and middlemen', who could help one in this manipulation of God, was both a cause and an effect of this new development. 

Now, back to the first question. If the Law of Karma is perfectly Newtonian and one can not escape the fruits of one's karma, then the scope for 'manipulation of God'  is diminished and belief or non-belief in Him becomes inconsequential.