Edit a sharepoint 2013 site in sharepoint designer 2013

1. only the root site of site collections will contain a style library, not subsites
2. You should find the style library upon site creation, but you can try enabling the publishing infrastructure feature and see if that helps
3. as a last resort, you can create a new site collection, and save the style library as a template and add it to your site that is missing it

as for editing, you should use sharepoint designer, although you do have the possibility of creating a mapped folder in windows by using the url of your website