1.- If I delete a segment in AAM that was pushed to a destination, the segment is also deleted in the destination or the segment need to be deleted itself from the 3rd party platform?
[Your understanding is correct. You need to manually remove the segments from 3P systems. However, there are a few 3P data platforms which allow deleting segment feature as well such as Google S2S destination but this is not the same for all partners.]
2.- A user qualified for a segment and I pushed it to a destination.
Now the user changed its behaviour and I want to delete it from the segment.
2.1- how can I purge that user from the segment in AAM? [To remove a user from a segment, you need to remove the same user from its respective trait. Once trait removal is done, the segment will automatically be removed from user's profile.]
2.2- when I purge it from a segment in AAM is it purged from the destination segment? do I have to make any special action? [If a user is removed a segment then data sent to the destination will reflect the same. No additional action required here.]
I hope this answers your query, please let me know for any additional question on the given matter.
Taking in account your answer, are you confirming that when I delete a user from a segment in AAM it is automatically deleted in 3rd party platform?
I understand that when you push new data this user wont be pushed, but what happened if the user was pushed in the past and belongs to the audience in the DSP or Adserver? Will it be purge in 3rd party platform segment?