If I achieve the Ego + 30 option on a mind control roll and give the command "Perish." Does the target take the d6 normal damage per 5 points rolled on each of their phases until they make their breakout roll, or only on the first phase after they fail their breakout roll?

 

Also, Is the target allowed to take any other actions on their turn? What if the command was instead to "Just die." or "Lie down and die."?

As Mind Control is an Instant Power, the target would take damage only on the first Phase after failing the Breakout Roll.  To damage the target further would require an additional MCV Attack Roll and an additional Mind Control Effect Roll.  As always, the GM may decide differently.  

 

Unless the controller specifies otherwise (such as with a control worded as "Do nothing but die" or similar), or unless the target actually falls unconscious or dies, the target would be able to take actions afterward.