Does the DA-42 automatically lean to clean fouled spark plugs?
Depends on the variant.  Most DA-42s are powered by turbocharged Diesel engines and do not have spark plugs.  And yes the DA-42 uses an automatic run up cycle in order to test the Engine Control Units (ECU).  The test button is depressed and held while the automatic ECU cycle runs on both ECUs for each engine; the pilot simply monitors the engine gauges for signs of abnormalities.

Now the DA-42L is an exception to this rule as it is powered by Lycoming IO-360 gasoline engines.  It makes use of more conventional run-up procedures.