D7: How do I modify the People Search page?

I'm new to Dolphin 7 but not new to PHP or CSS (I'm using D7 because I don't plan on going live until Q1 next year and wanted to start getting familiar with the architecture).  I need some help understanding how to modify the Search People section on the right side of the People Search page.  Basically I want to remove the "I am a: Man/Woman" and "Looking for: Man/Woman" from the Options, but I can't seem to wrap my head around how to do it or where these sections reside on the filesystem. I don't know if it's going to be an HTML snippet or PHP I have to edit.  I assumed it was an HTML snippet that I have to copy from base to tmpl_uni then edit, however I can't the appropriate file.  Is there a way to map these sections on pages to the proper resources that have to be edited?

Thanks in advance...

administration/fields.php  // search profiles

remove the unwanted blocks

Want to make it look pretty?

what is the page? search.php  open it

in it you will see:

$_page['name_index'] = 81;

this means templates/base/page_81.html is the template file it uses...yes you can add more divs and boxes etc

$_page['css_name']   = 'search.css';

means it uses this means templates/base/css/search.css

$oSearchView = new BxDolSearchPageView();

Thanks for your detailed reply, it all makes sense to me now.  I just needed a little nudge in the right direction and you've done exactly that.