Friction

There is friction in all of these instances.

Thank u, it will help me in my year end test

There is zero frictional force in the first instance (the object is on a flat surface).

Think about it this way. No matter what the table is made of (i.e. if you reduce the coefficient of friction to zero), the object isn't going to move since there is no force acting on it in the horizontal direction.

And now a friction joke:

A: Knock knock!
B: Whose there?
A: Interrupting coefficient of friction.
B: Interruption coeffic....
A: Muuuuuuuuu

We can't say that frictional force has a zero value. If so, then the object will move forever in nonstop.

This is correct if the object is moving. But, in this case it is at rest (i.e. it is not moving). So yes, the frictional force has a zero value when the object is at rest.

What does Newton's First Law say?

What hasn't been mentioned so far is 'starting friction'. It takes more force to overcome starting friction when at rest than an objects coefficient of friction when moving.

The term you are probably looking for is "static friction". There is a force exerted by static friction in case three (since gravity exerts a force that is not perpendicular to the surface which is balanced by the "static" frictional force). Because the block remains at rest, you know that the net force is zero. This means that there is a frictional force balancing out the parallel component of the force of gravity.

In case one, gravity is perpendicular to the surface. So the frictional force (i.e. static friction) is zero.

I'm not sure we're talk'n about the same thing, but I'm too lazy to look it up right now.

I am talking about the science of Physics.

Maybe we can both be happy with this version:

Definition of stiction
:  the force required to cause one body in contact with another to begin to move