Even though one mind is saying that I should not think of any bad activities like Kama, jealousy, etc., there is always another mind some how goes in the wrong way. Is there any way I can avoid this dual thinking?

You will have to understand that lust, jealousy etc. are inborn and are very difficult to overcome in a short period of time, although eventually we will have to win over them.
It is not dual thinking. The ‘manas’, based on the ‘vasanas’ (impressions) tend to generate those thoughts and the intellect (‘arivu’) issues warnings. That is it.
For instance, a sugar-patient is tempted by sweets because of his ‘manas’. At the same time, his intellect warns him against taking them, and says that he might get into complications.
Whether the mind or the heart wins – that depends on his will-power. And, undoubtedly, strong will-power can be attained only by constant prayers.

I have heard some people narrating their dreams, wherein they speak to God or chant His Names. I don’t get any such experiences. Can you please explain?

According to ‘mano shastra’ (the science of the Mind), whatever went deep into our consciousness during our waking state will only be reflected in our dreams. If your Bhakti or the Mantra you chant has been ingrained in you so deep, then you will witness them in your dreams.
That apart, a few people can have the Saintly people, Devatas, Pitrus and the Lord appear in their dreams according to their wish. However this is very very rare.

My mind is always restless and sensitive to worldly matters. During the darshan of my Satguru, it remains peaceful and calm. At other times, it keeps oscillating, even during japa, dhyana etc. I am tired of this state of mind. What should I do?

As long as you think that the Guru is a physical form, you cannot attain the peace of mind you desire. Guru is not a physical form. Try to meditate and concentrate on His form, and you shall definitely attain peace of mind.

When the mind dies, do all the memories go away or does it become insignificant? Can I understand this way that the mind comes under the control of the person who kills the mind?

The Body, Prana, Intellect – all of these are ‘Jada’ (lifeless). When the mind dies, it is simply not possible for one to identify oneself with these. When the mind dies (when one realizes), he doesn’t identify himself with the body, prana or the intellect (which are ‘jada’ or lifeless). It is so, only for others who view him as his body and its related sheaths.
Let us assume that you knock the door of a house and the householder asks who is at the door. You say, ‘Naan’! (me!). Again comes the question from inside, ‘Who is that?’ and you respond, ‘Naan thaan!’ (its me, myself) to make your identity clear.
Here you are mentioning two things – the first ‘Naan’ refers to your body, and the second ‘thaan’ refers to the Self. When you wish to make your identity clear, you unknowingly say ‘Naan thaan’, stressing on the ‘thaan’, the Self.
In this context, Ramana Bhagavan, in His Aksharamanamalai says,
‘Thaane Thaane Thaththuvam idanai thane kaattuvaai Arunaachalaa’
When the ‘Thaan’ (Self) reveals its presence, the ‘Naan’ (body) is no more significant and the memories, intellect, body etc. which are all related to the latter don’t exist anymore

What should I do to purify my thoughts and get Sri Sri Swamiji’s blessings?

In Bhagavat Gita, Sri Krishna says I purify those devotees who worship me by way of chanting the Maha Mantra. So, by chanting the Maha Mantra, you are automatically purified and at the same time, get Sri Sri Swamiji’s blessings too.

How do I control the mind and divert it towards Bhakti?

Chanting the Maha Mantra mechanically is the Sadhana. When this is continuously done, in due course, you will start chanting it while you enjoy the sweetness of it. This is the ‘Sadhya’ (the result which is Pure Bhakti).
Hence by merely chanting it will make the mind divert towards Bhakti. No additional ‘sadhana’ is requried for controlling the mind or diverting it.

I feel, mind is like a monkey which wavers, making concentration difficult during prayers or chanting. How do I overcome this?

The elephant cannot keep its trunk stationary. It keeps swaying it always. In order to arrest its movement, the mahout gives it a huge chain to hold on to. Similarly, in order for the mind to concentrate, we have it focus on the divine Name and Form of the Lord. That is the basic principle of idol worship. Instead of going for a multitude of Names and Forms, it is advisable to stick to one deity and chant one Mantra incessantly. This will bring concentration and one-pointedness. One can thus achieve eternal bliss by merely chanting the Maha Mantra.

I am not able to concentrate on the Nama or God, even as I chant the Maha Mantra. What is the solution to this?

This is normal. The mind is always trained to move outwards, towards the world. It is just not easy to have the mind concentrate on something for a while.
Then how can concentration be achieved?
When we continue to chant the Maha Mantra, in due course of time, the power of the Divine Name will automatically give you the concentration that is required.

I want to be totally free of sins and become joyful and cheerful, bring happiness to everyone in life. Knowing the questioning and doubting human mind, how can one ever get conviction in God, know Truth and become free?

Unless you experience the truth yourself, your doubts will not vanish. Great saints like Lord Buddha, Swami Vivekananda, Ramana Maharshi, J. Krishnamurtiji were terribly attacked by various puzzles, and their sincere quest led to their realization.
Before clarity, there is bound to be confusion. You should not stop with confusion. You must proceed in a divine path suitable to you and really verify for yourself, if the results experienced by these saints are really true.
Chanting the Maha Mantra incessantly with steadfast faith, patience and perseverance will help you achieve what you want.
It is heartening to note that you will stick on to the Japa and pray to the Lord to fill our hearts with love and noble thoughts. Its indeed the greatest prayer. We are very happy for you. Lord Krishna will bless you bountifully and will ever be with you in your spiritual quest.

Are the thoughts coming into the mind from outside or do they arise from our consciousness?

The stimulus (triggers) come from outside and they take the shape of thoughts inside us.