If a man knows that he being under a suffering or joy for this specific Karma he has done in the past, he would take that as a lesson and would start leading a life free from evils. Why are we (normal people) not provided with that power?

Civil, criminal and social laws dictate that certain actions are right and certain actions are wrong. For every wrong act, a punishment is ruled, and the nature and severity of the punishment differs based on the nature of the crime. Hence it is enough if the Government spreads awareness among the public about the laws. Imagine what would happen if the Government decided that all the citizens be taken to the prisons to see the punishments that are being undergone there.
The already confused man would panic and lose his morale. One’s self confidence will touch such an abyss that he will be scared to do anything at all, based on his visual experience!
So, cognizance of something is entirely different from experiencing or visually witnessing it.
God gave us the Shastras through the Mahatmas that help us decide what is right and what is wrong, just like the laws of the land in our example. It is for us to believe in them and follow them.
In the world, every moment, we witness that there is suffering on one hand and joy on the other. What more lesson do we need on the Karma Theory?

As per Hinduism, we take birth in this world due to our Karma (Deeds or misdeeds in our previous generation) So many deaths occur due to natural calamities where thousands of human lives are taken away. Man made calamities on account of bomb blasts also take away precious human lives. What is the sin or the Karma these human beings have committed whose lives have been plucked by the Almighty in few seconds of such calamities?

It is true that we take birth according to the karmas of the past births. Regarding the lives lost, it is not possible to find out the karma of each and every person and account for the same. But one thing can be said for certain. God is perfect. An imperfection cannot come from the perfect.

If everything happens according to the Will of the Lord, then why does the individual get affected by his actions whether good or bad?

You are right. Everything is controlled by the Lord and no atom can move against His divine will. When that is the case, when something good is accomplished by you, why do you take credit for it? That is because of the sense of ‘I’ or ego which comes into play. As long as that feeling exists, it is impossible to believe, in the true sense, that you are not responsible for anything – good or bad.

Sometimes, when we see people suffering from problems, we attribute it to being the effects of the sins of the previous birth. What would have happened in the very first birth, when there wouldn’t have been any ‘previous’ birth and hence no merits or sins associated?

Yes. In the very first birth, everybody was given all the amenities alike and good health and happiness alike too. Then, it is because of each individual’s greed that they started committing sins.

What is the difference between God and Karma?

Karma is the ‘Jada’ (lifeless) and the bondage. God is the pure Consciousness and Supreme Self and is free from all bondages.

It is stated that a true Mahatma will not punish the person who caused him harm. If that is the case, then who will punish him and make him realize his mistake?

Mahatmas never punish. But the power that is responsible for the functioning of the entire cosmos will punish.

Why do we get sufferings in life? Why can’t God create a world that has no sufferings, or better not perform Creation at all, at the first place?

Let us assume that someone comes to me and I tell him that I am his saviour and that it is me who has been protecting him so long. He immediately would ask me for explanation. I go to say that as per his karma, he should have died at this point of time or some accident should have befallen, but I have nullified his bad karma and protected him.
Even if this were true, the person would laugh at me and call me a bluff. But, if he encounters a dangerous situation and comes out of it without any problems, it is then that he would realize the truth.
It is easy to question after an event has happened, but our mind does not realize the invisible protection that keeps away harm. That is quite the nature of the mind.
So, if there is no suffering, we don’t realize the protection. That is why we get sufferings.

Why are human beings punished for the acts of their previous births, when everything is pre-destined? What is the role of God here?

The destiny simply decided based on the acts of the previous births. God is like a judge that administers justice in a court.

Why do God fearing people seem to suffer more than others?

A doctor administers anesthesia only to a patient who needs to undergo an operation. Likewise the Lord blesses with Bhakti, those people who need to work out their severe Karmas so that the effects of their severe karma do not affect them much.

Is karma applicable to animals too? Is there any difference on karma effects on man and women separately?

Karma is the same for men and women. As for animals, the animal birth occurs only to experience the effects of the karma carried over from the previous birth. During the lifetime of the animal, the karma is not accumulated.