I don't know if this is possible, but can a door family read the rating of a wall and also have it read in the door schedule? I have tried applying a shared parameter on the door family and adding it in the project. I am not understanding how I can link the two together. Please help!
No. That relation wall-door in regards to the fire rating is not available through parameters in the way that you have described. A common solution is to handle this via visibility graphics, as a way to have a visual control of the fire rated values of doors and walls.
It is possible via API tools but it is all custom programming. There is no "out of the box" solution for this. There is a video of an AU presentation showing how this can be done at this blog site.
The part talking about what they did in the API to read the fire rating of the host wall and apply a value to the door is at about 38 minutes into the video.