@Florence: For detail customization like this, you need to post in your site URL so that I can check in and suggest you css.
1. That page take the category title followed by Category Archives: . So, if you want to edit the title then edit the category name. But if you want to edit “Category Archives:” then you need to build child theme. For child theme, refer to http://catchthemes.com/blog/create-child-theme-wordpress/ and then copy archive.php file to your child theme and edit that.
To remove the border in that title, you can add the following css in “Appearance => Theme Options => Custom CSS” box:
.page-header { border: none; }
2. Archive and search are the default widget if there is no widget in the sidebar. So, go to “Appearance => Widgets” and drag and drop widgets as per your need in your sidebar which will replace the default widgets.
3. Sorry I don’t get it what you mean. Title of the post is always above the content of the post.
4. To hide entry meta, you can add the following css in “Appearance => Theme Options => Custom CSS” box:
.entry-meta { display: none; }