form in a .tpl.php file
Given your definition of studiga_theme_theme(), Drupal will never call custom_add_property_form() because there isn't any relation between the theme template you define, and that function. Eventually, you could implement the preprocess function for that theme template, and set there a variable that is passed to the template.

function studiga_theme_preprocess_add_property_form(&amp;$variables) {
  $variables['form'] = /* define here the form */;
}


Now your theme template will get a $form variable. 

Keep in mind that, except in a case, themes don't define forms; that is the task for a module. Eventually, themes can alter a form provided by a module, but (generally speaking) you will never see a theme that defines a form that is not for its own settings.