How much of our initial conditions come from past Kamma? When we come into this world, in a rebirth, how much of our situation is predetermined by our past Kamma? I think I have some understanding of the role of inherited Kamma in our personhood. But, are there teachings which indicate if our genetic makeup (good or poor) and our initial social/economic situation (born to rich or poor circumstances) are influenced by it?

To ask in another way, does a person with negative Kamma have a likely-hood of being born with worse health and in poorer circumstances than one with positive? Or are these 'random' factors, uninfluenced by Kamma? Or is this an unanswerable question?

I sense these are unrelated but I have not found guidance yet in this issue.
Buddha addressing the issue of Kamma in the Chula-Kammavibhanga Sutta (Majjhima Nikaya No. 135) has shown us why “No two people are alike and why human beings differ in their skills, beauty, longevity, health, personality, etc..”. It was in response to a question asked by Subha. Subha asked as to why no two human beings are alike? Why some people are short lived, and others long lived, some sickly and others healthy, some beautiful, and others ugly, some influential and others non-influential, some rich and others poor. In response Buddha said:


  ” beings are the owners of their own actions, born out of their actions, related through their actions, and have action as their arbitrator.  Action is what determines and differentiates beings in terms of their processions, character and the qualities they inherit.”


From this we can take that the effect of ones past kamma determine the nature of ones present situation in life. As I pointed out before, everything is NOT due to Kamma. Kamma is one's own doing reacting on oneself, and so one can divert the course of Kamma and the degree to which depends on oneself. Only the Buddha had the perfect knowledge about kamma. He is the only one who fully realised kamma. He is the ONLY one who could teach the nature of kamma, how it works, how it originates, how it is eliminated. For you and me, it is too complex an issue to try to understand. For example, ONLY when a person gets married that for him/her all hell would break loose and the marriage end in divorce. That person can never find contentment in marriage even in subsequent marriages to others. Then there are those who can never find success as a recluse/bhikku. That is their Kamma. Thus from a Buddhist standpoint, our present mental, intellectual, moral and temperamental differences are mainly due to our own actions and tendencies, both past the present. So in short yours is an unanswerable question.

AN 3:76 Bhava Sutta: Becoming, gives us an analogy to describe how becoming is produced:  “Kamma is the field, consciousness the seed, and craving the moisture.” Kamma gives us a range of possibilities in which the seed of consciousness can be planted and on which it can feed. Craving is the moisture that keeps the seed alive and allows it to grow into a state of becoming. 

Then there is this aspect too. Kamma can mean different things in different contexts. Once Buddha said that “Intention, I tell you, is kamma. Intending, one does kamma by way of body, speech, &amp; intellect.” — AN 6:63. In others, kamma means also the results of that action. The six sense media (Ayatana) are old kamma. Whatever kamma one does with the body, with speech, or with the intellect: This is called new kamma.” — SN 35:145. kamma is complex because the relationship between old kamma and new kamma is intertwined. It is so complex that that past kamma does not absolutely determine one’s experience of the present moment. There is a tendency for a certain type of kamma to lead to a certain type of result, but the intensity of that result is not a fixed thing. It is also influenced by a factor of present kamma: one’s state of mind now when a particular instance of past kamma ripens. Thus the kamma of one’s state of mind in the present moment plays a crucial role in influencing how the ripening of past kamma is experienced.