Can I move contents/widgets that are attached to another content/widget across stages?

Yes, you can move content/widgets that are attached to other content/widgets across the stages.

Here's how content/widgets can be moved across stages,

Content movement across stages

If a content is used in any other content, then Whatfix notifies you about the linked content and helps move both the main content and the linked content together across the stages. In such cases, Whatfix does not allow selective content movement. This enables content creators to provide a smooth user experience and reduce the chances of content breaking for the end users.

For example, if you have two flows inside a branched flow, then you must move all the three flows together across stages. If the linked content is not moved across each stage together, then there is a very high likelihood of broken flows and poor user experiences.

Similarly, if a content is used in any other content, then you cannot move it back from Production to Draft until you move the main content as well.
For example, if you have two flows inside a branched flow, then you must move all the three flows together from the Production to the Draft stage as well.

Widget movement across stages

If a content is used in any widget, then Whatfix notifies you about the linked content and helps move both the widget and the linked content together across the stages. In such cases, Whatfix does not allow you to selectively move a widget. This enables content creators to provide a smooth user experience and reduce the chances of content breaking for the end users.
For example, if you have a flow attached to a Pop-up, then you must move both the flow and the pop-up together across stages. In case you move the pop-up without moving the flow then the pop-up will break for the end users disrupting their experience on your application.

Only the Self Help and Task List widgets can be moved independently across stages even if the attached content is not moved along with them.

Similarly, if a content is used in any widget, then you cannot move it back from Production to Draft until you move the widget as well.
For example, if you have a flow attached to a Pop-up, then you must move both the flow and the pop-up together from the Production to Draft stage as well.