Is it possible to export TM with tags which were created during project translation or added to segments after import?
It does not matter how the tags have been created, once the TM record has tags, they will be visible in the exported TMX file
Is it possible to export TM with segment ID in xlsx?
It is not possible, the segment ID will not be visible in the generated xlsx file (please see https://jira.xtm-intl.com/browse/XP-34933). The segment IDs will be visible in the metadata if you generate a TMX file.
Is it possible to export segments from TM containing a specific word?
It is not possible to export these, you can only search for them in TM Manage tab.