At the moment VE only allows parameters to be added and deleted. Rearranging parameters is sometimes needed to place them in a more logical order (title before content). Editing the field names without having to delete and then re-add is also a must.
Description
Description
Related Objects
Related Objects
Event Timeline
Comment Actions
This is already possible with TemplateData editor; the order is dictated by the paramOrder array field, and can be edited in the editor. The name of the parameters can also be edited in the editor, and changes when the user applies.
This can be done per template when the templatedata (which is already required for information about fields in VE) is edited.
Comment Actions
Fields are shown in the community-set order in the TemplateData, as Moriel says.
Renaming fields is T52268: VisualEditor: Let users relabel (or renumber if auto-numbered) parameters in the transclusion dialog.