Dear Denis,
The button on the screenshot looks like it is a part of a third-party plugin, and not the theme; plugins usually have their own stylesheets included, which is why it is very difficult to style every single one of them from inside the theme, so themes are responsible only for styling their own files. However, if you provide the URL of the page with the said button, I can help you style the text – I just need to see the live code.
As for the image slider – it does not show up on category pages because it is not meant to by design of the theme :) However, by including one line of code into the “category.php” template file it is possible to make the header appear on category pages as well – I’ve done that for you, check out the page in question!