I have some news for you:
I made a totally new installation with version 1.4.4.3. The installation stopped at the point, where you have to create a new user/password. PHP Log shows the following error: Call to undefined function hash() in /home/mywebspace/public_html/zenphoto/zp-core/lib-auth.php on line 1224. The errors mentioned before showed as well (ENT_SUBSTITUTE + PHP_MAJOR_VERSION). No way to get further.
So I made a local install with XAMPP. Here the installation stopped at the point, where the database tables should be created. Following 2 errors were shown:
Notice: Use of undefined constant ENT_FLAGS - assumed 'ENT_FLAGS' in C:\xampp\htdocs\zenphoto\zp-core\functions-common.php on line 294
Warning: htmlspecialchars() expects parameter 2 to be long, string given in C:\xampp\htdocs\zenphoto\zp-core\functions-common.php on line 294
Finally I downloaded Version 1.3.1.2. Installed locally without problems, could create Users, uploading files, all perfect.
So I installed the same version to the onlie-Server: all works fine. Then - just for fun - installed the upgrade to version 1.4.3.5: same problems as usual.
Seems that the new version and my server / pc aren't good friends... Online Server Info: PHP 5.2.3, MySQL 5.0.45. Local Server Info: PHP 5.4.7, MySQL 5.5.27.
I don't know what's wrong with the new version. But at least I found a solution that works for me.