I'd strongly suggest you either use .htaccess to not allow users to read your directory or add a blank index.html file to the directory.
What I do not see are any vbulletin files - just some of the directories. I'd suggest you reupload all the default files, and import a backup database and see if that fixes the issue.
if you delete all files you lose all members and posts in other words you install from new
Deleting the files does nothing to the data, as long as you have a copy of the database you won't lose your members or posts. Deleting all the files and re-uploading them will however make sure that any changes the hacker made have been removed.