The situation is not entirely clear to me. You are talking about Property Manager but these are not ARCHICAD Properties you show on the image, they are IFC Properties. The red X means you can delete them. This can happen only one way: if you created these IFC Properties here in this Beam Dialog. When you create a New custom IFC Property, there is a checkbox that lets you create that IFC Property at the specified level of the IFC hierarchy, which means that the IFC Property will be available for all similar elements (for example, elements classified as IfcBeams). But in that case there is no red X, and you can delete that IFC Property only in the IFC Scheme Setup Dialog.
So you did not create any ARCHICAD Property in the Property Manager, I think you selected some Beams and created these custom IFC Properties in the Beam Settings Dialog, making these IFC Properties available only the selected Beam elements.
Maybe your scheduling problem stem from this but I would have to see screenshots about your Scheme Setup Dialog and the generated Schedule to see what is going on there.
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