If the dot product between the ray direction and the plane normal is greater than zero then it indicates that if you're going to collide with the plane at all, you'll be hitting the back of it.

Exactly what behaviour you want to take when a ray hits a back face is up to you. By reversing it, you're essentially making your plane double sided, which might be desirable, it probably depends on your usage case. You might want to be able to see through the back faces, or to ignore them because you have another plane at the same location but pointing the other way with different material properties.

Taking steps like precaclulating dot product results because your ray's direction is always 0,0,1 sounds like it might be a premature optimization at this stage. I would get stuff working before you put in special optimizations that take advantage of your ortho projection.

Yes, you should be able to ignore the reverse procedure if you don't want back faces to be visible.

Just remember whenever you're investigating why something isn't visible, that one of the many possible explanations is because you're looking through the back of the surface.