Yes it is quite well-known that he did. You can find it being mentioned in this PDF (Swami Vivekananda - A
Biography by Swami
Nikhilananda), on pp 190.
At the end of an hour his hands trembled a little and he breathed once
very deeply. There was a silence for a minute or two, and again he
breathed in the same manner. His eyes became fixed in the centre of
his eyebrows, his face assumed a divine expression, and eternal
silence fell. 'There was,' said a brother disciple of the Swami, 'a
little blood in his nostrils, about his mouth, and in his eyes.'
According to the Yoga scriptures, the life-breath of an illumined yogi
passes out through the opening on the top of the head, causing the
blood to flow in the nostrils and the mouth. The great ecstasy took
place at ten minutes past nine. Swami Vivekananda passed away at the
age of thirty-nine years, five months, and twenty-four days, thus
fulfilling his own prophecy: 'I shall not live to be forty years
old.' The brother disciples thought that he might have fallen into
samadhi, and chanted the Master's name to bring back his
consciousness. But he remained on his back motionless. Physicians were
sent for and the body was thoroughly examined. In the doctor's opinion
life was only suspended; artificial respiration was tried. At
midnight, however, Swami Vivekananda was pronounced dead, the cause,
according to medical science, having been apoplexy or sudden failure
of the heart. But the monks were convinced that their leader had
voluntarily cast off his body in samadhi, as predicted by Sri
Ramakrishna.
As regards your 2nd question, i don't really know whether he gave any reasons or not.
UPDATE:
From pp 105 of the book "A short life of Swami Vivekananda by Swami Tejasananda":
The Swami was thirty-nine years and a few months, thus fulfilling a
prophecy which was frequently on his lips, ‘I shall never live to see
forty.’
So, he must have said that to many people and on many occasions.