Looking on some rss apps in store, i found out, that some of them allow to user to type text in search rss editbox, and then show the list of founded rss feeds.
How does they do that?
Is there exists some free public api, for searching a rss feeds??
Yes, they use different APIs for that, check out Google feed API for more information.
Here's the developer's guide. It's pretty straightforward: https://developers.google.com/feed/v1/jsondevguide
I'm actually developing a RSS APP for android myself, don't hesitate to ask me anything should you need some help :)