Look at this answer by Chip Bennet – Medium / Large images sizes aren’t cropped by default ( and I also just verified on my install ). You can change the cropping of Thumbnails in Settings -> Media. It sounds like what you really need is just a new image size via add_image_size() which is also described in his answer.
As far as removing unused images, right now you’re probably out of luck – you’ll need to go backwards and remove any unused images by hand ( maybe there’s a plugin out there, I’m not sure ). There a few ways to keep your WordPress clean, I prefer to delete associated media whenever a post is deleted. Charles Clarkson and t f have good answers for that. If you only want to target only the Featured Image you can look at these answers by sanchothefat and Ravs.
Really though it may be better to break you question into more specific questions to get more specific answers instead of grouping your 3 questions into one.