How to reproduce drupal.org search?
This is not so much an issue of suing Apache Solr as it is one of working with the database query system.  To do what you want you will have to become very familiar with the Views module.  I recommend watching the nodeone.se series 'Taming the Beast' 

Views is a UI for making sql queries.  You create a view definition with a path you assign to your look-up page.  It will include filters to sort content by types.  The various categories of information at Drupal.org are basically different content types. The various displays lists etc. used to provide the information can be provided by a variety of modules.  I would recommend exploring Panels and Page Manager to provide and display the information.  Nodeone.se also has an excellent series called 'Learn Page Manager' that can help you master those issues.

If you want custom functionality and know your way around PHP you may want to look at the Drupal Forms API, the Search module, and Search API module for additional functionality in creating customized searches and forms.