Is it possible to use navigation stack for local navigation only?

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If you have the map of the environment already you can use amcl only for localization.

If you do not have map, you can use gmapping for SLAM.

Either way, navigation stack provides you 2), 3) and half of 4) in your question. You should make your sensor readings ready in your system (possibly via /scan topic), this is not a responsibility of navigation stack. Then, it will process sensor data and identify obstacles, planner will generate optimal paths regarding obstacles and finally move_base will output necessary vehicle velocities (longitudinal, lateral and yaw velocities). After this point you should calculate wheel velocities according to your vehicle model and generate PWM signals with your hardware. This part is not covered by nav stack.

Therefore to my opinion, you do not need to limit nav stack. Instead you should supply missing parts and configure nav stack correctly for your purpose.

You may need to go over nav tutorials for implementation.