Ok, after solving my first problem, I got very similar warnings:

Warning: file_put_contents(/home/dho/projects/myproject/tmp/cache/models/dbomysql_companies) [function.file-put-contents]: failed to open stream: Permission denied in /home/dho/projects/cake/cake/basics.php on line 751

That was easy to fix, I had to set the “write”-Permission for the user used by Apache (on Linux this means to use the following command: chmod -R 777 /applicationcontext/app/tmp).

Update 2008-03-02: Adding the chmod command to make the tmp folder writable, thanks to Juan!