Removing index.php not working on hosting althougt all conditions true

It should be in public.

If you installed CodeIgniter in a subfolder, you will need to set RewriteBase appropriately.

I tried to manipulate with it, but received only "500 Internal Server Error".

Well, it is preconfigored by hosting multipage version, so the app is in a subfolder in fact. But since it is preconfigured on the server I don't think it is a problem.