Even by following the same routine, the condition of the mind is different on different days. What are the factors those make the mind disturbed on some days, joyful on some?

In Yoga and Vedanta Shastras, these concepts are explained in great detail. To put it in a nutshell, Vasanas and their provocations are relevant reasons for this. It takes consistent, persistent, long practice to attain one-pointedness of mind.

Adi Sankara says that intellect (koornda madhi) can be used for Realization. But Bhagavan Ramana says that the answer to Self-Realization cannot come from the mind, and that the thoughts (mind) need to be killed. One seems to be using the mind, while the other is aiming to kill it. What is the difference between the two?

With the sharper intellect grows the ability to discriminate between the real and the unreal. As long as you are not convinced about the what is real and what is not, your desire for Realization will not get serious. When the ‘viveka’ (sense of discrimination) of the mind improves, you will get closer to the Truth. Eventually, when realization dawns, even the mind will vanish.
Bhagavan Ramana gives a wonderful illustration in this regard – one of ‘Pinam chudum thadi’.
the interrer (‘vettiyaan’) in the cremation ground stands by the side of the burning corpse. Owing to the heat, the corpse rises up on its own accord every now and then. He uses a stick to beat down the dead body that rises. Finally, when the body does not rise up anymore, he throws the stick also into the fire. In the same way, a sharp mind aids in Self-enquiry to find the Truth and is itself eventually destroyed.

I Beg to know, how to control our mind to refuse sensual indulgence at least when it affects our health and duties.

The mind is enslaved to habits. So it will not obey you if you order it to stop doing something that it has been accustomed to. It is only by constant practice that one can get rid of habits. The best way to overcome it is to chant with patience and perseverance.

Why are few days so disturbing and horrible in life? It is so difficult to sit and pray in those days. Mind plays havoc and goes wild. Then, suddenly it becomes easy to differentiate and becomes controllable. Then worship and prayer becomes possible. Why does this happen? Please help.

Just as the body gets tired with headache or cold, the mind also experiences these swings like a disease and hence goes through such cycles. You need not worry about such swings. Chanting of Mahamantra will slowly reduce the frequency and bring everlasting peace. But it will take some time and you have to be patient.

On many occasions I feel I am intimated in advance by some force of incidents before they actually happen. Why does this happen?

This might be due to the merits that you had acquired in your previous births.

My mind always has lewd thoughts. How do I control it?

Whenever you get such lewd thoughts, watch keenly as to who is getting those thoughts. When you keep on continuing the enquiry, you will find an answer to the ‘I’. Concentrate on this ‘I’ and meditate on it incessantly.
During the rest of the time, chant the Divine Name ‘Hari’, ‘Hari’, ‘Hari’ constantly. Your thoughts in that direction will reduce considerably.

I have been practicing meditation for about two months now. But my mind wavers from trivial matters to lustful thoughts, though my eyes are closed. Am I doing it right? Please guide me.

You have started on the right track. There is nothing wrong in your practice. Continue with it. However patience and perseverance are paramount. Initially you put in the efforts, and eventually grace takes over. Hence, you will come to witness slowly that the situation changes for the better.

I feel restless, get negative thoughts and end up with frustration on myself. I lose concentration in my studies and only after a long time do I regain it back. At times I feel that I don’t chant Nama sufficiently. I want to chant the Mahamantra more and more with more love towards Krishna.

When chanting the Nama, it is incorrect to observe the mind. Concentrate on the Name, and the Named who is none other than Krishna.
Once a patient had a serious illness and he approached the doctor. After examining the patient thoroughly, the doctor prescribed a set of medicines. Immediately the patient said, ‘I am averse to taking these medicines. Please give me some medicines that will make me amenable to take these pills!”
So, chant the Divine Name. That is the solution to everything. Wake up from slumber, come out of your laziness, realize the truth and chant the Nama. That will show you the way.

What is the difference between Manas and Budhi?

The intellect [buddhi ] and the mind [manas ] are not physical organs. The mind [‘manas’] is nothing but a collection of thoughts. Thoughts owing to imagination and impressions of observed objects constitute the mind. Emotions like fear, anger, lust, etc. are dimensions of the mind. The intellect [‘buddhi’] is that sheath which is responsible for analysis and rational discrimination based on previously known facts.

I have observed that it is very tough to keep the mind free. I used to think too much and then get in to unnecessary trouble because of the same. I feel that the mind can be streamlined. Can you suggest the way?

First of all, it is important to understand what is mind. Mind is nothing but a collection of thoughts. Other than thoughts, there is nothing called mind.
Now, the next question is, how do these thoughts rise?
Thoughts rise because of Vasanas. Vasanas are nothing but latent impressions – impressions created deep inside us because we have been repeatedly doing certain activities for a long period of time. It is only when one is in deep sleep or when one is sedated that his mind does not function. During all other times, it is active. This is the nature of the mind.
Having thus said, it is also important that you don’t let your intellect watch the mind all the time and worry about your current state. This will create a complex in you, making you either guilty or proud and over-confident. So it is best not to police the mind.
Don’t mind what mind does.
The elephant cannot keep its trunk still. 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 streamline its thoughts, we have it focus on the divine Name and Form of the Lord.
By chanting the Mahamantra either mechanically or whole-heartedly, the complex can be overcome and the thoughts can be streamlined. The Mahamantra has the power to do so.