So what exactly you don’t know?
Before inserting the post, query all your posts and check if the values are the same. if they are not, insert your new post in the database, else display an error or something.
To display the name of the taxonomy, no matter what taxonomy is:
$value = get_query_var($wp_query->query_vars['taxonomy']);
echo get_term_by('slug',$value,$wp_query->query_vars['taxonomy']);
Happy wordpressing 😉
I found the solution here: http://wordpress.org/support/topic/pagination-with-custom-post-type-listing?replies=23#post-1637753
Seems like you cannot set the page and custom post type with the same name.
Thanks!