How to show results from the last search?
You could try Search API Saved Searches Module


  This module offers users the ability to save searches executed with
  the Search API module and be notified of new results. Notifications
  are done via mails with token-replacement, their frequency can be
  configured both by admins and/or users and saved searches can also be
  created without first executing the search.
  
  Facet, Views or other filters set for the search will also be included
  in a saved search, thus reflecting exactly the same search results as
  displayed.