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… Can you ever be free of fear?
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… What is your final fear?
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Final fear - loneliness
I don’t know if one can ever be free of that fear, considering that there’s always a possibility that those close to you will disappear. That doesn’t mean you have to experience the fear at all times though.
Yes
I’m not exactly sure what you mean by this. Do you mean fear in a normal sense, or fear as a psychological abnormality?
If you mean “Is it possible not to be scared by anything?” the answer is yes. However, this is a situation which is unnatural and to be avoided at all costs. Fear is a healthy and useful adaptation. Fear prevents us from performing many behaviors which are likely to have negative effects. For instance, many people are afraid of heights. This leads them to avoid behaviors like walking along the edge of cliffs or climbing over protective railings, behaviors which place us at considerable risk of falling. Fear is also very useful in telling us which situations are threatening; if you’re walking alone down a dark alley in a crime-ridden part of town, your fear is telling you this is not a good idea and you should get to safety as soon as possible. It prevents you from taking a leisurely stroll through a war zone. In this respect, fear is an incredibly useful adaptation.
It is possible, through injury or defect of certain portions of the brain, to be incapable of feeling fear. This is all-around a bad situation. Suddenly, many important inhibitions disappear: without fear, you may start walking along cliff-edges and charging blindly into other dangerous situations. There is a part of the brain called the amygdala, which when removed in laboratory rats, causes them to lose their natural fear of cats. This makes them have no reservations about walking right up to a potential predator. You can see how this might be a bad thing. I’m not aware of any research on humans relating to the perception of fear as a function of the brain, but maybe a wiser and more well-read doper will come along shortly with some more info.
If you are referring to fear as a chronic and abnormal psychological state, this is most certainly not healthy, but it can be treated. There are many mental illnesses in which fear, especially irrational and unfounded fear, play a large part. Panic disorders, for instance, cause brief episodes of intense panic in sufferers, often for no clearly discernible reason. I have personally dealt with this disorder, and it can be treated- I’ve had great success with prescription anti-depressants, namely Paxil. My chronic and irrational fear has largely disappeared. But too much fear, or fear of the wrong things, can have near-crippling effects. Certain phobias come to mind- agoraphobia, or the morbid fear of open spaces, often leads its sufferers to live the lives of hermits. They are unable to leave their houses with exeriencing extreme panic, and as a result, they cannot hold a job, be social, or any of the other things which most people take for granted. This is most certainly maladaptive, but it can be treated with both medication and therapy.
I’m completely lost as to what you mean about “final fear”. 
As my field of study for my tenure in college and grad school was psychology - environmental psychology at that - and is my current form of employment at a small liberal arts college in new england I would say the final fear you are asking about is death.
I have always told people that being afraid of the final fear is like being afraid of your bed at night. Unless you sleep on leaves and branches high up in a treee you do find some place when the sun goes down to rest your head. It is inevitable. A bed or resting place is inevitable, so why fear it. Death is inevitable. For all you know it is a wondrous part of our lives, one some people actually look forward to. I have read quite extensively on the subject and found that most people who experience death can not wait for it to happen again, they say it is one of the most pleasurable experiences they have ever had. In a battery of 4000 sick and sometimes terminal patients who have experienced near death exeriences or actually dies and come back, nearly all of them reported a very good feeling associated with the process of dying.
In this book Madelaine Lawrence shows detailed analysis of the 4000 patients she studied and through her research into the unconscious found a great correlation between death and a general good feeling when it happens.
That said I would say conquering fear does not have to involve medication and could easily be obtained through yourown stong will or with the help of a behaviour therapist. Behaviour therapy allows one to take controll of the therapy and have a more involved approach to their illness and subsequent cure.