WordPress.org

What is the recommended image size?

Any number at or below the size you chose for thumbnails within the admin panel. This will help minimize bandwidth usage and allow for faster loading.

How can I add Featured Posts to my homepage only?

Place within your index.php but outside the loop.

How can I add Featured Posts to a specific category?

Place within your categories.php file (or index.php file is categories.php doesn't exist).