Do bit.ly and other URL shorteners reutilize unused short URLs? It seems the be so. Is there any risk that an URL that is redirected to a certain page right now, be redirected to another page in the future?
At least for bit.ly, the URL associated with the short link can't be changed. It's a security feature because, otherwise, someone with bad intentions could theoretically take over an account and replace all short URLs with malicious destinations.
Can I edit/change my bitly link? What if I email you and ask nicely?
bitly links cannot be edited. They also do not expire and cannot be changed, so they will always redirect to the site for which they were originally created. It's always a good idea to check that your long URL and/or custom name are correct before creating, sharing, or printing your bitly links.
It is provider specific, check the policies of whatever provider you are using. Goo.gl allows you to keep the URLs ye shorten and track usage. Bit.ly does not allow them to change. Tiny URL never expires.