DB cache_filters entry for sin(z)/(x^2+y^2) not found.
This does not necessarily indicate any problem. The DB cache_filters is updated only when you enter algebra expressions within Moodle itself, eg. within a forum, not when you enter an expression in the debugger.
What happens when you click on the "Show Image" button? If an equation image is shown, then your algebra filter is working properly.
If "Show Image" doesn't work, what error message do you get? Then try the "First Stage Tex Translation" and "Second Stage Tex Translation" buttons and tell us what happens.
You should not need to make any modifications to httpd.conf or to algebra2tex.pl. [An early development version of the filter did require modifications, but not the current release version which came with Moodle 1.2.] Also you should not move any files -- all files should remain in the filter/algebra directory.