Can I post without categories?

Question

Taxonomy

If you do not specify a category in the post, uncategorized will be added. You cannot remove it from the categories of this post, only if you specify some other category/s.
1. Is it possible to do something so that a category is not added (ie, so that some posts are without categories at all)?
2. But if the url uses categories, can you make it use other taxonomies to build the url?
3. Is it possible to specify the priority of other taxonomies when building a url?