It seems Adobe InDesign has trouble importing QuarkExpress documents properly or even at all. However you can find some commercial plugins like Q2ID that allow users to import .qxd files properly to Adobe InDesigns. It is not the cheapest solution however.
Convert QuarkXPress document to Adobe InDesign graphics document file.
We found 4 software records in the database related to .qxd to .ind file format conversion.
Microsoft Windows software - convert qxd to ind on Windows
Professional desktop document publishing software from Adobe
Convert from qxd file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned qxd to ind. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
A plugin for Adobe InDesign that add support for QuarkExpress files
Apple macOS / Mac OS X software - convert qxd to ind on OS X
Mac version od Adobe's popular document designing and publishing software
A plugin for Adobe InDesign for Mac that add support for QuarkExpress files