How can I edit my search box I want to customize my search box. I want it to auto complete as I type and not to be case sensitive. What should I do to achieve this?
For the autocomplete search box, there is a fantastic module Search Autocomplete with a detailed installation guide, and also has functionality such as integrating Views and Transliteration modules (which will overcome special characters/capitilisation etc.)

There is also a Patch for an exposed filter that may be of some assistance (if you are using a custom search box that you have made) that will help with the "contains" or "contains any word" operator.