How can you preserve URLs when moving posts to a custom post type?

You can’t. Permalink rewrite rules are a set of patterns that the URI is matched against. If they all share the same pattern, one will always take precedence, so you will only have a single post type that will not 404. Categories (or some other taxonomy) is the way to differentiate content that shares the same URL structure.

Hata!: SQLSTATE[HY000] [1045] Access denied for user 'divattrend_liink'@'localhost' (using password: YES)