Warm Start Problem and Slow Down light - related??

You should (and should've) measure the fuel pressure after engine shutoff to see if the residual fuel pressure falling to quickly is what is actually causing the warm restart problem or not. In addition to the two most common causes that you have already addressed, the third possible cause is a bad o-ring seal inside the fuel pressure regulator that can also cause the residual fuel pressure to fall too quickly -- but make the measurement!

Completely unrelated (and a false signal as a cat can't overheat instantly). Most likely a bad warning light ECU, but can also be caused by bad thermocouple connection(s) or an internally "open" thermocouple.

 

The slow down light is related to the thermocouple which in turn connects to an ECU. You can remove the thermocouple from the cat and use a brass wire brush to clean it up, it can have deposits caked on that apparently can alter the readings. Also put some Deoxit on the wire connector that connects it to the slow down ECU.

In my owners manual it notes that when starting the car when hot, you have to slightly press the accelerator. This is because the throttle position sensor on the throttle body has a different signal sent to the main fuel injection ECU when the car is at rest and started cold. When starting hot, you want the TPS to be just off its rest position. The TPS can be out of adjustment, it slightly twists on its two mounting screws to be set up such that a very slight click is heard just off idle. You can check this by moving the throttle body lever on the throttle body (engine off), and test for that click just as it is moved from rest position.

May not be your problem, but easy to check.

 

No -- that's the Pulsation Damper. The fuel pressure regulator is part of the fuel distributor on the K-Jet system. See this thread for pictures/descriptions:

https://www.ferrarichat.com/forum/posts/148352872/

Post #9 has a good picture of this damaged o-ring.

Did you actually measure the fuel pressure at warm engine shut-off and confirm the fuel pressure is dropping too quickly?