newtonian mechanics - What's the motivation behind the action principle?

1. 
   

   What's the motivation behind the action principle?

   
   


2. 
   

   Why does the action principle lead to Newtonian law?

   
   


3. 
   
   

   If Newton's law of motion is more fundamental so why doesn't one derive Lagrangians and Hamilton principle from it?

   
   


4. 
   

   Also does all Lagrangians obey $L=T-V$?

   
   


5. 
   

   I think that it's related to the fact that the kinetic energy of the particle at all points on the path or it's travel time is as small as possible?

   
   


6. 
   

   If so, How can we derive the principle of least action from this fact in detail?