Do experiences with precognition and fortuitous instances come more as as a warning to those who encounter them?

That would be a useful survival adaptation. A fairly common story is the one about having a feeling that even though you had the green light you felt you shouldn't go. Then a speeding car ignored a red light and flew through the intersection, a car that would have caused a bad accident had you gone. I imagine insurance companies are fond of such premonitions. 

Even if certain events are predicted in advance by Psychics, Mediums, Spiritists, no one will be able to avoid that event, it will happen!

Because only God, can do it, in his power!

Some prophecies have been averted because people took the better advice.

9/11 tragedy, people not going on those flights or even to work at the towers is an example.

Related:

The Path of the Higher Self;

Autobiography of a Yogi (has examples).

If precognition really does tell you the future, then there is nothing you can do about it. What will happen, will happen. So what good is a warning?