Can i add custom search form for different pages ?

I’m trying to add custom search form for different pages, for example:

* I have a team page, and every member has a lot of specification ( department, language, nationality, … ) so i want to add to this page search form and check box to fillter the search.

also i have news page, and want to search maybe for an author or specific newspaper, …..

so it there any way to use a widget or something to do that, thanks.