Dear Kari,
I will reply in the same order:
1). You can alter or remove the “Category:” text by manually editing the “category.php” file found in the root of the theme (line 11); to center the headings you’ll need a CSS declaration:
.category #blog-header h1 { text-align: center; }
2). Category pages are in essence filtered archive pages, thus anything that is possible on the latter can be done here as well. You can either edit the “category.php” file or use a third-party plugin to insert the required content.
3). In WordPress, this is how the post number limit functions – it applies to all blog and archive pages. Circumventing this is a bit more complicated, but can be done, of course. To display a custom number of posts on category pages, you’ll need to create a custom wp_query loop and tell it to show a particular number of recent posts. This article contains the relevant information. I can help you set up the query, yet I will have to charge for that since such changes in template files are considered theme customization. Alternatively, you can use a third-party plugin and insert a shortcode that would display a custom post list filtered by category, e.g. this one.
Sincerely,
Andrew / Satori Studio