The relevant policies for your question you'll find here: https://developers.google.com/places/policies
you may use the searchbox and you also may use the results to show them on a page without showing a google-map
it's still not clear if you use any type of map inside your application, but when you do so, you may not use any data delivered by the places-service to use them on this map(e.g. you may not use the latLng of the place-result to create a marker on this map)
you must show the google-logo (because you show data -name and address- received from the service)
when the response contains html_attributions for the place you also must show these html_attributions
