Using pages instead of posts will eliminate the dates yes. You could also modify your template file to remove (or comment out) the <?php the_time(); ?> or <?php the_date(); ?> which will remove the date as well.
If you have all of the same information on the new page/subpage and the url remains the same then there would be no need for a 301, this would actually cause a redirect loop as the page would be trying to redirect to itself.
Categories are only used for posts and not for pages, so yes once you have moved the post to a page you could remove the unused category as well.
