Is It Always Possible To Read A Person's Mind By Looking Into His/her Eyes?

No, not unless you have some special powers and can read fortunes, and even then, some people can mask their feelings, and others not.
Some people are even able to convince themselves, and in turn, the world around them, that they are as innocent as a lamb, and that the people they hurt or destroy are willing victims, and actually deserve what they get.
So I think it is a little dangerous to think that you can always read people's minds.
There are people that are very open and honest, and if you know them, you can predict with a fair amount of accuracy, what they are thinking, but not always.
However looking into a persons eyes is the best way to communicate, as often the mood or attitude, and even the soul of a person, are seen in their eyes.

Yes.All you have to do is look at their body language.

I think it is very well possible because it has happened to me

No. I have not even been in the room with someone and "read their mind". And no I am not a medium. In Acadian or as you might call it "Cajun" it is called "Tres Terre"

Yes it happens to me with this one guy I can always look at him and know what his thinking

This is not entirely a myth, because according to FBI and police training methods, during interrogation eye contact is an important area to monitor.  Here's a link you might be interested in

www.kinesic.com

The logic here is quite reasonable.  If people break eye contact, there is some psychological avoidance.  If people access the creative side of their brain, they will tend to look towards one directioni, and if they access the memory side of their brain, they will look in the opposite direction.  Hence eye contact maybe an important factor to consider, given the proper assessment of the condition of the person in question

I'm part NDN and a real cowboy and can even read dogs and cows eyes, too!
logic101