Hi,
1. I’m afraid no, the content has to be accessible locally, within the current WordPress database.
2. You can get access to the search data via the WP Rest api, there is an endpoint to run queries directed to ajax search pro.
I would probably setup the website with the search. On-site search is done with that step. Within the APP I would make a search bar and make it run queries to the rest API endpoint, then process the results within the APP as needed. I suppose mobile APP frameworks (like Unity) have libraries to make fetch requests and process JSON data, that is univerally used. I believe that is the simplest, easiest and most robust solution – as queriying the REST API endpoint will not break with updates.