What are the stories/facts behind the origin of word Hindu? Another Question , What is the life vision of a Hindu?
Hindus didn't call themselves Hindu. It was the name given by Islamic invaders. To them everyone living beyond the river Sindhu were Hindus including Buddhists, Jains & animistic tribals. Sindhu becomes Hindu in Persian and Indus in English. And the land of these people beyond Sindhu became Hindustan.
To the native, i.e ancestors of today's Hindus, their religion was just called Dharma. Dharma came in many flavors like Sanathana Dharma with it's various sects, Buddha Dharma & Jina Dharma with their sects..
With regard to your first question, Swami Vivekananda said (Complete Works, V3, "Vedantism" - http://cwsv.belurmath.org/volume_3/vol_3_frame.htm):
The word Hindu, by which it is the fashion nowadays to style ourselves, has lost all its meaning, for this word merely meant those who lived on the other side of the river Indus (in Sanskrit, Sindhu). This name was murdered into Hindu by the ancient Persians, and all people living on the other side of the river Sindhu were called by them Hindus. Thus this word has come down to us; and during the Mohammedan rule we took up the word ourselves. There may not be any harm in using the word of course; but, as I have said, it has lost its significance, for you may mark that all the people who live on this side of the Indus in modern times do not follow the same religion as they did in ancient times. The word, therefore, covers not only Hindus proper, but Mohammedans, Christians, Jains, and other people who live in India. I therefore, would not use the word Hindu. What word should we use then? The other words which alone we can use are either the Vaidikas, followers of the Vedas, or better still, the Vedantists, followers of the Vedanta.
With regard to your second question, the "life vision" of a Hindu is escape from this endless round of births and deaths. What is meant by this escape varies between the different sects.