Is character facing in the direction of camera?

How could I check if the character is facing in the direction of the camera or away from it?

This answer will depend on how you define facing and away and the orientation of the camera with respect to the player’s ground plane, and whether the ground is flat. If you are just looking for within a 180 degrees:

var dot = Vector3.Dot(transform.forward, Camera.main.transform.forward);

if (dot <= 0.0) {
    Debug.Log("The character is facing the camera");
else {
    Debug.Log("The character is facing away from the camera");