Zenphoto tries to set permissions to 0755 for directories and 0644 for files. If that does not work, you have the possibility to set different values during setup.
Please also see: http://www.zenphoto.org/news/permissions-for-zenphoto-files-and-folders
Permissions being set to 0000 is for sure something that happens server side.
Also, Zenphoto only tries to reinstall when something has changed in your installation or in the server software.
I'm afraid you will have to contact your host again.