Which template or include file in Omega subtheme takes hook_form_alter()?
The preprocess.inc and process.inc files are an Alpha/Omega way of organizing template_preprocess and template_process functions.  Basically, if your template.php would have a mytheme_preprocess_node, you would put it in preprocess-node.inc and name the function mytheme_alpha_preprocess_node.  When you clear cache, and Drupal rebuilds the registry, the Alpha hooks will scan all of these files and wire everything up.

This doesn't mean that everything else that you put in template.php goes in these includes.  Your custom theme functions and alters should still stay in template.php.

This can help keep the size of template.php managable, but I always still end up with large files because typically needs lots of theme and alter functions for the projects I work on.