New search widget

Hello.

I want to create a new search widget that only displays results from one category. I do not want to do anything with the standard search widget but I want another one as well. Any ideas on how to do this?

Also, I am wondering about how to redirect users to a page if they type in the same title as the post. For instance: the user searches for “hello” and this redirects them to: http://www.mysite.com/category-name/hello. I basically want do the same as for instance http://www.thefreedictionary.com/ (try to search for a word there), but with the category-name in the permalink.

It would be fantastic if anyone could come with any suggestions, tips or thoughts about my questions.

Thank you so much!