3D camera orientation

You could try first placing the camera's Point of Interest where you want the camera to always point, then with the camera selected you go to the menu Layer / Transform / Auto Orient... then choose the Orient Toward Point of Interest option. If this isn't exactly what you're looking for, it will at least give you an idea of how to make it.

I hope this helps.

2D layers are always perpendicular to the camera. I'm not sure I understand your concept. You can auto-orient a 3D layer to the camera, tie the Camera/Point of Interest to a null with a simple pickwhip expression, and then animate the null to the center of different 3D layers to get the camera to look at a new spot. 

Maybe a sketched storyboard would help us help you figure out the simplest way to approach the problem. It might be easiest to parent the screen recordings and any graphics you add (3d layers) to a 3D null, keep the camera still, and then move each layer into position by simply animating the position and rotation of the null linked to each screen recording.

I often find it easier to think of the Comp Panel as a stage and decide where I will put the actors and how to move the camera than just to start moving layers around in 3D space with no real plan.