Permalinks and displaying categories on a custom headlines.php?cat=3

I use WordPress as a CMS.

With the default URL structure, I can do things like
site.com/article.php?p=100 (displays article with id 100 in a custom article.php file)
site.com/headlines.php?cat=3 (displays a list of articles belonging to that category in that custom file)

I switched to permalinks, I properly configured them, I can now display posts as site.com/article.php?p=100 or as site.com/article.php/category/yyyy/mm/dd/post-slug

Question 1: site.com/headlines.php?cat=3 for displaying titles in a certain category doesn’t work anymore. How can I have a page like that where it displays headlines from a certain category only?

Question 2: How can I remove the article.php from site.com/article.php/category/yyyy/mm/dd/post-slug? I uploaded it as single.php but that doesn’t seem to do the trick.

Thanks for reading!