How can I update the markers when moving the map?

So basically you want to listen to the map changes and every time the user is dragging the map and reload the results? Here's what you should do:

public class AwesomeCameraActivity extends FragmentActivity implements
        OnCameraIdleListener,
        OnMapReadyCallback {

    private GoogleMap mMap;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_my_camera);

        SupportMapFragment mapFragment =
            (SupportMapFragment) getSupportFragmentManager()
                    .findFragmentById(R.id.map);
        mapFragment.getMapAsync(this);
    }

    @Override
    public void onMapReady(GoogleMap map) {
        mMap = map;

        mMap.setOnCameraIdleListener(this);

        // Show the initial position
        mMap.moveCamera(CameraUpdateFactory
                .newLatLngZoom(new LatLng(YOUR_LATITUDE, YOUR_LONGITUDE), 10));
    }

    @Override
    public void onCameraIdle() {
        // The camera / map stopped moving, now you can fetch the center of the map
        GeoPoint center = mMap.getProjection().fromPixels(mMap.getHeight() / 2, mMap.getWidth() / 2);
        double centerLat = (double)center.getLatitudeE6() / (double)1E6;
        double centerLng = (double)center.getLongitudeE6() / (double)1E6;

        // Now fire a new search with the new latitude and longitude
        searcher.setQuery(new Query().setAroundLatLng(new AbstractQuery.LatLng(centerLat, centerLng)).setAroundRadius(5000))
    }
}