How to use WordPress REST API v2 to search posts?
I did something similar to what you are describing for a WP/bbPress android/ios app. First, I made my own wordpress search api end point to hit. Then on the wordpress side I used a custom mysql query to query post titles and post content for the search string and return that to the api.
I made the query only return 25 results as I didn't need to have more results than that, with pagination and such.
You can use Search Results REST API Endpoint to seach by keywords you provide.
For example http://yourdomain.com/index.php/wp-json/wp/v2/search?search=lorem&per_page=5&page=1 will search for the keyword lorem in your wordpress posts.
Per_page : limits the number of results per page