Generates a simple sitemap for your site.
Pages are listed according to 'menu order'. When you edit pages, you can set the Order. There are plugins available which let you drag/drop pages to set your preferred order.
Yes - if you have pages & subpages, they will be listed as an indented list.
No. Posts are listed from newest to oldest, and are not grouped by category.
No, I haven't build that feature yet.