From the main body of the document a search should continue into headers and footers, yes.

As you have seen, you can't use ^d REF in the "Replace with" box. If you want to replace something with a particular field, just copy the field to the clipboard and specify ^c in the "Replace with" box.

No, when using ^d or ^c you shouldn't select the "Use wildcards" option.

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Stefan Blom
Microsoft Word MVP

Microsoft 365 apps for business
Windows 11 Professional