Nice writeup,
I think all of the requirements are supported in terms of lucene capability, and you can create those searches manually in the little search box today.
But this of course needs a search form.
I would like to put some emphasis on the search results list as well. The current search results list is just to plain simple. It needs
-Configurable columns
-Sortable columns
-Optional output format (like cvs, pdf etc)
-Optionally action menus - Take direct action on an item instead of having to go the the details page
-Filter kind of items in results