Selecting the taxonomy terms to use using a textfield to search them My Drupal 7 site has almost thousand of taxonomy terms. So it is a hard work for my users to pick their desired category from thousand of taxonomy terms.

Is there any way to select a taxonomy term by using a small search box to choose the exact category and sub-category?
You can try using Views to build a custom search with exposed forms. And the use the fields to display terms the way you need it. That is probably the easiest.