Changing the permlink and SEO

You can check the status of the redirect using any number of developer tools (chrome can do this by default). I believe the default redirect that wordpress does when the post title is changed is a 301, but I could be mistaken. If you need finer control (or would like regex support), the Redirection plugin is a great option, and it supports 301, 302, 307, and 404 codes out of the box.