Yes, you can do this. You’d want to use conditional tags (such as is_category) to determine which category you’re in, and, if so, show the image associated with that category. Example
<?php
// if we're in a category
if(is_category()):
// get the name of the category
$category = single_cat_title('', false);
?>
// get the image with the same name as the category and display
<img src="<?php bloginfo('template_directory ');"/images/<?php echo($category); ?>.jpg" />
<?php
endif;
?>
See also: is_category, single_cat_title, bloginfo
It could be done via a child theme and some custom functions + a custom header.php template file.
I made a page that looks like I want the category to look, but I want it to work like a blog.
possibly create a page template for it; http://codex.wordpress.org/Pages#Creating_Your_Own_Page_Templates
with a custom query for the category posts; http://codex.wordpress.org/Class_Reference/WP_Query
it might help if you post a link to your site to illustrate the look of the page.
you can use a ‘featured image’ with a minimum width of 1000px to act as a custom header for any static page.
Thank you, I will try the template. I can’t have a blog on a static page, can I?
alchymyth has a really good idea and a better implementation. If you create a custom page template, you can tell it to display posts. It’s more involved from a coding perspective, but overall much cleaner.
Yes you can. See a page of posts for examples.