If I delete and reinstall Pages will I lose my files?
If they are stored in iCloud Drive or another remote storage thing they will be redownloaded when you re-setup Pages. If they are not in a Cloud storage thing, they will be deleted with the app.

Since iOS 9 is a bit old at this point, newer iOS have a files app and you should be able to store all your Pages and iWork documents in file storage as opposed to storing them in the application bundle to avoid deleting any documents when you remove the Pages app.