To remove the Headline, you’ll need to edit your theme’s files. You’re looking for a section that looks like:
<div id="top" class="clearFloat">
<div id="headline">
<img src="https://wordpress.stackexchange.com/questions/3456/images/headline.png" width="75px" height="21px" />
...
Delete the <img src=.../> line and the word “Headline” will disappear.
The drop-down menu can be repaired via CSS. Right now you’re facing a positioning issue. In your stylesheet (/wp-content/themes/arthemia/style.css) find the section of code that defines the navigation bar (#navbar). You should see this already defined:
background: #2C2C2C url(images/navbar.png);
margin: 15px auto 0px;
margin-top: 15px;
margin-top: 15px;
padding: 0px 10px;
text-transform: uppercase;
You need to add the following two definitions:
position:relative;
z-index:100;
This will tell the browser to position the navigation bar relative to its original position (which doesn’t change anything) but also to place it 100 layers above everything else. The drop-down menu will then render on top of your slide deck.