Removal of certain areas

Hello again!

Finally my last post (for now). I’m also trying to find a way to remove 2 sections from the ‘Add New Post’ or ‘Edit Post’ pages.

In either page, towards the upper right corner there is a section called ‘PUBLISH’ which contains several options such as Status, Visibility and the option to publish.

We’d like to remove the ‘Visibility’ option from this section. How might I access this area to do so, again without affecting base source code directly?

Second, in the ‘Categories’ section where you normally select categories, there are two tabs (at least on mine) called ‘All Categories’ and ‘Most Used’. We’d like to remove the one called ‘Most Used’. Any thoughts on this one?

Thanks everyone in advance for any insight you can offer!