Noindex Search Results Pages and Nofollow Search Navigation
You should noindex your own search results pages as they are generally lower quality, but you can disallow them if they are causing a problem with the server load from being crawled. You can nofollow links on the search navigation to prevent crawling but you should probably have followed links on the results pages which can be useful for finding new pages if they are crawled.
Limit Indexing Internal Search Pages
You can index internal search results pages, provided they are generally useful to users and are limited to specific terms.
Valuable Site Search Results Pages Can be Indexed
Google will crawl site’s own search results pages if they are linked, and may index them if they show content which Google thinks is valuable.
Google Can Use Site Search for Discovery
If Google can’t crawl a site normally because of a lack of internal links, and it can detect a search form, it might try to find new URLs in the site search results by running searches.
Markup Doesn’t Make the Sitelinks Searchbox Appear
Adding the Sitelinks Searchbox markup won’t help you get the box. But it may help Google get the configuration right if they are showing it.
Exclude Form Based Search Results Pages
Exclude your search results pages which can be reached through a text search form.