Controlling custom URL structure within a WP site?

Hello. I would appreciate direction on how handle managing custom URL structure. I need to so in order to maintain links from a previous non-WordPress site. So, for example, since I currently have permalinks in the dashboard set to "Post name" (/%postname%/):

This URL

would need to be modified to

While, single-view posts, would need to be modified from


So, basically "category" should never show in the URL, but single-view posts should show the actual category name that post is contained within. Can all this be readily handled from the permalinks settings in the dashboard, and if if, I'd really appreciate some guidance on how to?

Thank you!