normal force
Normal force
The normal force \[F_{n}\] is the component of a contact force that is perpendicular to the surface that an object contacts. In this instance normal is used in the geometric sense and means perpendicular. A person standing still on a platform is acted upon by gravity, which would pull them down towards the Earth's core unless there were a countervailing force from the resistance of the platform's molecules, a force which is named the "normal force".
Now, the phrase "perpendicular to the surface that an object contacts" is important. When force brings two solids toward one another and they are prevented from moving into the volume occupied by the other there must be another force involved. This implies that the normal force is the force which resists an attempt to cause two solids to occupy the same space. As such it points perpendicularly to the surface of contact; because motion along the surface of contact is not interpenetrating.
Newton's third law
Newton's third law tells us that when two bodies interact, they apply equal but opposite forces on one another.
Whenever we apply this, we have to be consistent about the two bodies that are considered.
The weight is the force that the gravitational field of Earth as a whole applies to the box. It has nothing to do with the ramp. By Newton's third law, the box also pulls the Earth up a tiny bit, but usually that is ignored as it is a very miniscule pull.
So the interaction we're concerned about is between the box and the ramp. The box pushes down and to the right on the ramp, and the ramp pushes up and to the left by an equal amount. That satisfies Newton's third law.
We choose to decompose the weight vector into components along the ramp and perpendicular to the ramp in order to make it easier to calculate. The box is not accelerating through the ramp, although it may slide along the ramp. That tells us that the force components directly into and out of the ramp must be balanced, i.e. they must add to 0. Only the components along the ramp may or may not be 0, depending on whether or not the box is sliding.