What are the triggers of the MD-80's takeoff configuration warnings?
There are 7 conditions, not 5. The two you are missing are:


AUTO BRAKE
This warning is when the auto brake system (ABS) has detected a fault, or the system is not activated.
AUTO SPOILER
This warning is when the spoilers are not armed when the ABS is set to takeoff.


What flap setting triggers the warning?


  Flaps lever position does not agree with selected position in computer window.


Why slats and flaps have separate warnings?

While the flaps/slats handle is the same, there could be a mechanical reason the slats failed to extend properly, or a circuit breaker is pulled. Also historically, the earlier DC-9 from which the MD-80 is developed, had a handle that could be physically separated.

What stabilizer setting triggers the warning?

Same as flaps, when the position disagrees from the selected one in the computer (it varies from flight to flight based on the different conditions).



Source: MD-80 FCOM Section 6 Pages 76–77