Is my understanding of Inertial Navigation Systems correct?

the inputs of the system are inertial movements of an object (car). it outputs acceleration (from accelerometers) and attitude (yaw, pitch, roll - from gyroscopes). it is then processed and analyzed to compute for the movements the object had done. With an initial coordinate(starting location), the data may be used to find for the corresponding coordinates of the final position.(longitude, latitude, etc)... is my understanding correct?

Answer:
You are close.

As a matter of fact, the "analysis" includes double integration of the accelerations. Integrating acceleration once gives speed and integrating speed gives displacement. The INS computes and sums these displacements (in all three directions). These displacements can be used with the initial frame of reference to get the current position.
Except for the word "(car)" it all sounds perfect. That system need not be just for a car - could be plane, ship, sub, rocket, etc.
Yes, except for the integrator.
That never works, except in a physics lab.
Basically yes, but you forget that the acceleration is processed into directional vectors and the position is the resultant vector extended over time.
A clock must most definitely be included.

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