A prism is a polyhedron (many faces) formed by (1) a polygon with n sides called the base, (2) a congruent copy of the base polygon that does not lie in the same plane as the original copy which is also called a base, and (3) sides, which are parallelograms, that connect the bases.
The prism is named for the bases. Thus if the bases are triangles, then you have a triangular prism, if the bases are pentagons then it is a pentagonal prism, etc...
In general, placing the prism on one of the sides (the parallelograms connecting the bases) does not change the bases. So in this sense orientation in space does not matter.
There is a special case however. Consider the parallelpiped. This is a polyhedron formed by 6 connected parallelograms. In this case you could consider any pair of opposite sides as the base. (Picture a rectangular box or cube. You could name the top/bottom as the bases, or front/back, or left/right sides as the bases.)
No, the bases of the prism do not change if the prism is placed on one of its sides. While it is true that the base that is on the bottom is changed, merely turning a prism over does not change any of its intrinsic properties (such as volume, surface area). However, how the dimensions of the prism are named may change depending on how it is positioned. Which edge constitutes the length, the width, or the height will sometimes change depending on the orientation of the prism. For example, for a textbook laying down with its cover facing the ceiling, we would mostly likely say the height of the prism is however thick the spin is. On the other hand, if we turn the textbook so that the cover is facing us while seated, the height of the prism may switch to become how tall the book is.
No, it does not.
No, the bases of a prism do not change when put on its side.