i-contrast should be used as needed, if you noticed some areas of the photo are blown out (really bright) or very dark. A typical example would be a daytime landscape shot, where land is correctly exposed but the sky is blown out. It slows down processing, so in most cases it can be turned off.
Red-eye detection removes red-eyes from photos when you use the flash. It is a time saver. You can always manually do it later using any photo editing tool, but having the camera do it saves you the time. It's not perfect, but you can safely leave it on.
Scene mode is for people who want the camera to take the photo based on certain factors. When you use the camera on full auto, the camera knows nothing about the scene and has to guess how you want the image. In scene mode, you tell the camera how you want the image. For example, in Sports scene, the camera knows to use a fast shutter speed to freeze action. In Landscape scene, the camera uses a smaller aperture so more of the image is in focus. You should use the Scene mode if possible, but you shouldn't restrict yourself to picking the technically correct scene for the subject.