...it means that script execute some ArcGIS instruments (calculate, addField, intersect and so on), thеn it can be necessary to edit some tables manually (so script should be suspended), and then, when editing is over, other instructions must be executed
Can you break it up into separate tools/scripts? (Similar to Bruce's suggestion of tasks in Pro). Have the first script(s) do the calculate, addField, intersect, etc., all in one script or separated. Run you interactive edits. Then additional scripts to do the other tasks.
Although I haven't tried leaving an edit session "open" at the end of a script, do your interactive editing and then run another to close the edit session, it might be possible. Take a look at
Editor—Help | ArcGIS Desktop
(and don't forget to save at some point in there.)