2. If the karmic theory is right, is everything pre-decided and there is no free will. Is human being weak? And can praying to God, challenge the karmic theory, exhaust the effect of the bad karmas...  

The first question: I feel that though all this is an illusion, there is a law which governs it all. A very simple analogy can be drawn from maths. In maths, a unreal system of numbers called Complex numbers is used. These complex numbers have no significance as far the reality is concerned, they have no meaning. But, while analysing problems, we start with real numbers, use complex numbers as a tool and finally get the answer in terms of real numbers. Same is the case with us: We are the brahman, we have come in this unreal world to use it as a tool to reach back, and finally we end up being just brahman. But when using complex numbers, there are certain rules which have to be followed, they have their own mathematics and one sees almost all maths of real numbers applicable in it. Though complex numbers are unreal, they have rules to follow some rules, same is the world, our karma, though just maya, but follows a rule.

In the Bhagwad Gita, it is stated that it is us who relate with the karma, actually we are not doing it, but because we relate with it, we bear its burden. To be free from it is to simply detach from the karma. It is all a mental phenomenon, we face the consequences in the same reference frame in which our mind is. A simple analogy is to think that all of us are in cars moving with different velocities, viewing the world differently due to the same reason. Nothing is therefore unreal, but the same truth pictured by a different mindset, hence the law governing us are also dependent upon the speed of our cars. A paramhamsa, sitting in  azero velocity car may have no effect of the karmic theory while the one moving in the car, is being fully controlled by it. For this simple reason, some see the material world, some see Krishna everywhere and some just himself. The laws keeps on changing according to the plane of understanding and mental viewpoint.

Hence, I feel that advaita poses no contradiction to the karma theory, both are right, but working in different planes of understanding. They are like two non parallel lines but in two different planes!!!  

The second question: To address the second question, let us for some time, forget all our theories of Advaita. In the simple world we live in and which we see, two people born are unequal in many respects, in the socio-economic conditions, talents, qualities, colour, etc. A big question is why one peson born on this earth is less or more fotunate than the other. Here lies the basic thought which is the root of the karmic and re-incarnation theory. The first intutive idea is that he must be so due to his own deeds. That seems the only logical explanation. Of course, this explanation rests on the belief, that there is a logic governing this world and not everything is chaotic. But, also, faith is the stepping stone for a theory, it is then the initial inputs which forms the theory, and finally the theory is tested by time in various differing conditions. Had Newton not believed that there can be a relation between the moon revolving around the earth and the apple falling from the tree, may be Gravitation theory might have never come to existence. Hence the reincarnation theory builds from this point and as it progresses, it beautifully establishes a unity between all phenomenons.

Everyone has to pay for what he has done, that is the eternal law (In the reference frame he lives). If we have robbed someone in this birth. We will be robbed in our next birth. The thief reaches our house is not accidental but a masterplan of the karmic theory. And if we have not done anything wrong, no evil in the world can touch us. It is our own karma which hits us. Hence we are the all powerful, not doing anything wrong, we have the power to do anything, just anything.    

Continuing on the example in the previous paragraph, it is not that the thief has been pushed to steal at our house, it was his wish, the theory just decided upon the house, he has to rob. Hence there is free will, no doubts on this. Here we can see, the most beautiful reconcilation in the theory of karma and divine incarnation: When there is no practical mean to exhaust the karmic debt of the person (for example when no one was ready to fight with Ravan, there were no practical means that he be payed for his bad deeds), then the divine intervene takes a form just to mantain the karmic law and balance it, he is a non doer, just for this purpose he does karma.    

Moving to higher planes, makes this theory redundant, as the Bhagwad Gita states that a person who has no ego, has no accumulation of karma, and no binding of this theory.

Another doubt which remains is that if the Karmic theory is so right and stringent, how can praying to God stop mishaps. I feel that the misdeed have to be payed off, may be in tears of repentance or in agony of doing the wrong. I also feel, after reading a lot of books, that the realised (a Paramhamsa) has the power to tranfer the karmic debt of someone on himself. The debt is not destroyed, it is just transferred. Yes, it can only be destroyed by reaching to a higher plane of understanding and existence, even if it is so for a small period of time.

Some questions still revolve around the karmic theory, as to what results arw controlled by hard work (the immediate karma) and what by the past deeds. To be very frank, I don't have a 0 and 1 solution for this problem right now. I have ideas, but still trying to refine them.  

I hope I have made my viewpoint clear.