The red region I marked there the person hand is in contact with the block I want to know if there is any normal force acting between the person's hand and the block. If there is a normal force then what is direction of this normal force? If this person applies this force $F$ at an angle then will there be any normal force too?
The red region I marked there the person hand is in contact with the block I want to know if there is any normal force acting between the person's hand and the block.
If the person applies a force $F$ perpendicular to the surface of the block then $F$ is the normal force on the block. Per Newton's 3rd law the block exerts an equal and opposite force $F$ to the persons hands. If that force is perpendicular to the persons hands then $F$ is the normal force on the person's hand.
If there is a normal force then what is direction of this normal force?
The normal force is always the component of a force that is perpendicular to the surface.
If this person applies this force 𝐹 at an angle then will there be any normal force too?
Yes, but it will only be the component of $F$ that is perpendicular to the surface. If $\theta$ is the angle between the force and the surface, then the normal force is $N=F\sin\theta$.
Hope this helps.
The force labeled $F$ is the normal force from the hands acting on the block.
The word "normal" simply means "perpendicular to the surface" in this context. The force $F$ is perpendicular to the surface, so it is the normal force.
If the person applying the force is pushing at an angle, then you can still decompose $F$ into a perpendicular component and a tangential component. The perpendicular component is, by definition, perpendicular to the surface. So that component would be the normal force.
Adding to the other answers -
When the case is that only the block is on a frictionless surface - but the person is not (so the person can "push" the block without getting pushed backwards), even then there will be a normal force, which is the cause of the block's movement from rest.
To be more exact, the force will cause acceleration as long as it remains, which is very small here, because no matter the force, the block will move as there is no friction. So the contact will break from person's hands. And so there is no more normal force.
There onwards, the block will remain in constant motion as there is no force acting on it anymore, according to the Galileo's Law of Inertia (or the Newton's First Law).