Can the "Restore" button (in Web Domain > Backup > Existing backup) restore a deleted database? It seems like no.
No, when a database is deleted then it has been completely removed. You have to create a new database. If you have a backup file of the old database contents, then you can reimport that e.g. with phpmyadmin.
Thank you Till, I imagined. In this situation pressing "Restore" button you get the warning: "Restoring will overwrite existing files in your website. Do you really want to restore this backup?" and choosing "Ok" you get the message: "Restore of the backup has been started. This action takes several minutes to be completed." but the restore cannot be done. Perhaps it would be more clear not give these messages. Alternatively, still existing the user of database, it might be possible to recreate the empty DB and then proceed with the restore. These are just suggestions for future versions.
I am wondering about this as well. I ran into trouble yesterday attempting to upgrade the media module in drupal. My websites in ispconfig3 are drupal websites so I did a drupal backup/migrate backup of the website database, the database/corefiles/otherfiles and the extra files in my drupal web. Then I attempted the upgrade using the drupal upgrade path. As noted by others in the drupal community, it failed because of a dependency on another module (older one already present...therefore the new one would not install). I then attempted a restore using the ispconfig3 restore feature and after it is presumably finished, the display goes as far as the home page, but everything else is a white screen. When I used the ispconfig3 website restore feature of the web, I got the green notice that the restore is taking place, but it never seems to finish. If I go back into the website the same thing happens as with the drupal backup/migrate module - a good home page but nothing else. Can you advise what options I have now? Thanks in advance.
The restore is starting about a minute after you pressed the button and might take a few minutes to unpack the archives, so you might wait a bit. You can find details in the ispconfig log when you enable debug mode. Regarding drupal error, a white page is often a 500 error. Turn off custom error pages in the web site in ISPConfig, it might be that drupal can display a more detailed error message then and you might want to take a look into the error.log of the website.