'Car Status' doesn't work, no matter what I assign it to - a key or a wheel button.
This is the diagram showing tire temps etc.?
If so I have the same issue and it was also the same with F1 2012 - I wonder if it is because I only use cockpit view as it was there when I first went into the game but that was using a different camera.
I do turn off all the OSD options anyway as I want a more realistic view - I wish you could turn the red lights in the middle of the screen at the starts as well really and just view the real life locations.
I spoke with our QA team and I have some information for everyone interested as this is a lot more complex than you might think.

Below is what we checked and what you should try in your game.
I think there are a numbers of things which could have resulted in the problem being mistaken for a bug. We checked both an Xbox 360 controller and the G27 Logitech steering wheel (same as iMacken). We did not have the kext FFB file installed although this should not affect the testing results.
Firstly a single UI setting controls the display of car status. This is found in Options -> OSD -> Car Status and should be set to On to display. It is doubtful this is the cause of the issue for customers but for completeness sake I have included it as a possible solution. Note that the option is on by default.
Secondly not all modes support the display of car status, the UI will not appear in Time Trial proving grounds for instance. This is consistent through all camera views and is likely by design. Tire wear and full consumption are not in effect during these modes so there is no reason to display car status data. Testing against the PC the behaviour is the same. Note that engine mapping selection and tyre compound options are also removed in this mode (accessible from the Dpad on the Xbox controller)
Thirdly if mapping car status to the buttons on the face of the G27 wheel all 3 red buttons to the right of the steering column map as Button 7 and all 3 to the left map as button 8. If the user has attempted to map different actions to the 3 buttons on the right they will have remapped button 7 each time and left car status as "Unassigned" if this were the first mapped action. This could be quite easy to miss, although within the thread the user also suggests they have bound the keyboard keys to the action and still experienced a problem so in this particular circumstance it is not likely to be he cause of the issue.
We have confirmed that the car status UI appears in a single race in a number of car views (including cockpit) when using both the G27 and Xbox controller. Note that the G27 was set up as a "Custom" control config and the override input device type was set to "Steering Wheel". The controls were then set and bound manually.
From the main menu we selected Grand Prix -> Red Bull -> Vettel -> Default Race settings (3 laps Race only) -> Australia.
Once in control of the car on the grid the car status UI was able to be selected using the relevant button binding. Please can you try the steps above with Vettel and see if you see the UI as expected? If so it's likely just the mode you were trying doesn't allow or use the overlay you are trying to activate.