Yes, it is normal to not copy actions when copyong project.
Idea when copying project is to be able to copy its "structure", meaning thje Work Breakdown Structure.
This includes only the "planable" items.
There are 2 options, to copy :
1) main plannable items (activities and milstones)
2) other planable items (meetings, test sessions)
But not plannable items are not copied : actions, questions, decisions, deliveries, risks, ...
If you really need to copy Actions from one project to naothere, here is a trick :
=> export actions in CSV format (from list of actions)
=> change project in csv file and
remove id : this last point is very important to create copies and not change existing; best is to export csv without id..
=> re-import file : it will generate copies
IT'S A KIND OF MAGIC