How can I edit my search box
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.