Connecting the FSR sensor with the plunger rod as to transfer the full force
The FSR® Series Integration Guide seems to answer most of your questions.


  Does the force has to be applied to the single point in the active area or whole active area, ...? 


Section 2.2 states:


  This particular force-resistance curve was measured from a model 402 sensor (12.7 mm diameter circular active area). A silicone rubber actuator with a 4 mm spherical radius tip and 60 Shore A durometer was used to press on the FSR).


The silicone rubber tip seems like a good idea. These spread nicely and even out the force over the area while avoiding any sharp points.

Check section 7.0, Performance Optimization, which states:


  
  Start with Reasonable Expectations (Know Your Sensor)
  
  
  The FSR sensor is not a strain gauge, load cell, or pressure transducer. While it can be used for dynamic measurement, only qualitative results are generally obtainable. Force accuracy ranges from approximately ± 6% to ± 50% depending on the consistency of the measurement and actuation system, the repeatability tolerance held in manufacturing,and the extremes of the environment.
  
  
  Set-up a Repeatable and Reproducible Mechanical Actuation System
  
  
  Provide a consistent force distribution.
  Control actuator placement. 
  Keep actuation cycle time consistent. 
  
  


My reading of the datasheet suggests that you should manage your expectations with these devices. They are really touch sensors and not for force measurement applications where a load cell might be used.