how can I load the files when I open the modal 

You should contact the WP Post Popup support and ask them to add a possibility to include wpDiscuz plugins CSS and js files. 

which ones do I need? 

All wpDiscuz CSS and JS files. 

On our website, I am using WP Post Popup to open posts in a modal window from the homepage. But the modal isn't loading the CSS and JS files, which ofc makes sense since it's technically not a single post. 

But my question is, how can I load the files when I open the modal and which ones do I need? 

Thank you.