When an object moves in a circle it experiences centripetal force directed towards centre, But when we place an object on a disk which is rotating why does the object moves away from centre instead of moving towards the centre.
Short answer: It is because the centripetal force does not act on the body.
Consider the situation like this. Let us assume that the body is placed on a frictionless groove on a circular disc. Now, if you start rotating the disc, the particle does not feel any centripetal force. Now, consider a point just before our object under consideration.(towards the centre that is).
Since you had given the disc an angular velocity, the next instant, because of the centripetal force, the point before the body goes inward, while the body does not. A good way to imagine it would be like this. It is not the object that is falling away, but rather all the points on the disc are going inward because of the centripetal force, while the object, without centripetal force does not move along with them.
This means that the particles will separate, not because the body is moving out of the disc, but because the points on the grove are moving towards the centre, away from the body
An ultra-simplified version of the situation can be seen in the image below
Note that the ball does not experience any force towards the centre, the normal force pushes the body to the left, but not towards the centre.
It is not necessary,It is only possible if the frictional coefficient has value less than necessary to provide for the centripetal force, In the case you mentioned the friction coeff. is less thus the object can't have enough centripetal acc. to satisfy the circular locus the disc's periphery undertakes.