I want to remove “Search for” text from search form in TwentyTwelve, to wrap in in a div for styling, and probably to play with php a bit – and I’d appreciate some advice on how to do that best.

My “sub-questions within a question”:

1) Where is the main search function is located?

2) Should I create a separate custom file, add code to functions.php – or is it okay in this case to just edit the original search function?

Thank you in advance for your help!

Modify the searchform.php, or create one in a child theme (recommended), and you should be able to modify the form all you want.

This is the file that get_search_form looks for and is the file used by the default search widget, though it is not listed in the Template Hierarchy.

Reference:

http://codex.wordpress.org/Function_Reference/get_search_form