Dates are showing asterisks, but have no constraints.

Check external early start first, then external late finish. These are constraints created by P6 when subprojects are imported separately. This feature is intended to preserve the dates calculations between networks. In your case, because the way you are working (separate files) after you receive al subprojects, you need to recreate the relationships between them and then delete the external dates. To delete external dates, show these columns (Dates section) on the layout. Then click on the cell to edit or delete using the backspace key.