I have deleted my original answer, submitting the following instead in order to more directly answer your questions. In order to provide a more logical overall answer, I will answer your second question first.
2) Is it okay to take components of a force, find the acceleration in
the direction of that component and then further take components of
the said acceleration.
Forces and accelerations are vectors. Any vector can be resolved into orthogonal components. It doesn’t matter what the origin of the vector is, that is, the vector being resolved into components may be a component of a different vector.
But since gravity is only acting vertically downwards how can it cause
an acceleration in the horizontal direction. Is the Normal from the
surface of the incline the reason behind it. If so how?
Gravity is not causing an acceleration of the block in the horizontal (x) direction. As you have correctly surmised, it is the normal reaction of the wedge that causes the horizontal acceleration. To be more specific, it is the horizontal component of the reaction force exerted by the wedge on the block that is causing the horizontal acceleration of the block.
Fig 1 below shows the block sliding down the wedge. To the right of it is a free body diagram of the block. Per Newtons's third law, the wedge exerts and equal and opposite reaction force to the normal force the block applies to the wedge. Since the wedge is fixed, the structure prevents it from moving so that the net force on the wedge is zero.
The normal reaction force applied to the block is resolved into a horizontal (x) component to the right and an upward vertical (y) component on the FBD. The vertical (y) upward component is opposed by the downward force of gravity. The horizontal (x) component of the force is unopposed. It is the net force acting to the right and is solely responsible for the horizontal acceleration of the block.
Fig 2 summarizes the forces acting on the block. It shows the horizontal force acting on the block which gives it its horizontal acceleration, and the net downward (y) component of the force on the block, which gives it its downward acceleration.
From the equations we can make the following observations:
The maximum horizontal acceleration of the block occurs at an angle of 45 degrees and equals $g/2$.
The horizontal acceleration is zero at 0 and 90 degrees.
The maximum downward vertical acceleration of the block occurs at an angle of 90 degrees.
The downward acceleration is zero at 0 degrees.
Hope this helps.