[publish restriction plugin] Looking for a starting point

Hello,

I am creating a multiuser wordpress site for an online writers’ group.

I want to write a plugin which:

1. Allows authors to publish between the 1st and 15th of the month only.
2. Restricts authors from publishing more than x posts in a given category in that month.

To solve these, it should be a simple matter of inactivating the Publish and Update Post buttons (new post – wp-admin/add-new.php, quickpress – wp-admin/index.php, update post – wp-admin/post.php) based on a conditional statement.

My trouble is that I don’t know which hooks to use to achieve this goal. Suggestions please:

Thanks!