How do I fetch feed info from cache instead of directly from feed?

You could simply use fetch_feed() that implements it’s own extension of SimplePie_Cache:

$feed = new SimplePie();
...
$feed->set_cache_class( 'WP_Feed_Cache' );
...
$feed->set_feed_url( $url );
...
$feed->set_cache_duration( apply_filters( 
    'wp_feed_cache_transient_lifetime', 12 * HOUR_IN_SECONDS, $url ) );

that caches the feeds with set_transient().