Do an ajax search on a WordPress site

You need to do an ajax search on the site for arbitrary, customizable fields.

The site is powered by WordPress.
It's a Types plugin.

The site sells mobile phones, a link to the private to interested performers.

Work on integrating search was carried out, but the previous team was unable to implement ajax and cope with the process freeze when a large (many selected fields) request in the database.

It is necessary that the search work "on the fly" exactly as on the site example: Texte caché

Required fields to search as on this site: Texte caché