Culling in Display List

Is it possible to allow the display list to
do Backface culling, dynamically, as and when the scene is rendered.

Yes you can, with or without display lists.
Using display lists does not matter for backface culling, because OpenGL always transform vertices with the modelview matrix before backface testing, even in a display list. Otherwise you should not be able to perform essential operations such as translating (dynamically) an object before you call its display list.

After creating the Display list with all the polygons, irrespective of the
Front or Back Face, Is it possible to render only the front face polygons,
from the display list, by passing the current eye location.
The rendered front face polygons will change dynamically, as in case of rotation.

When you’ll call the display list, OpenGL will compute on-the-fly which faces have to be culled, using the current eye location. OpenGL will always cull what is invisble on current screen, dynamically. If you rotate (or translate) your object, then OpenGL will probably cull other faces, because the object projects differently on screen.

But the limitation is that OpenGL works with current “eye location”.
For instance, you can not cull polygons facing left or right. You only can ask OpenGL to cull what is facing/not facing the camera.

Again, using display lists does not matter. Results are exactly the same with or without display lists, at least in the case of culling.