I reuploaded everything, but kept the database... The frontend on every theme is still all over the place. Setup worked properly this time. Backend is nearly fixed, apart from some weird things regarding arrays, see http://mstratforddesign.co.uk/images/Backend1.png. (The view site button top right, the selector and the green text).
Setup.log:
Zenphoto Setup v1.4.5.8[676d2dec8b]: Thu, 02 Jan 2014 15:52:11 -0500
Query error: MySQLi not connected
Warn: zp-data security [is compromised] Zenphoto suggests you make the sensitive files in the zp-data folder accessable by owner only (permissions = 0600). The file permissions for security.log are 0640 which may allow unauthorized access.
Warn: PHP version 5.3.24 PHP Version 5.2 or greater is required. Version 5.4 or greater is strongly recommended. Use earlier versions at your own risk.
Warn: PHP display_errors [is enabled] This setting may result in PHP error messages being displayed on WEB pages. These displays may contain sensitive information about your site.
Debug.log is full of stuff, probably not best to paste here

I can email it if it is better!