1) How do I lower that main bar that’s going threw the banner, or how can it even be removed?
For this I'm fairly sure you are going to need to download and edit your layout.html file. You will need to either locate the table element that the banner is in and make it taller. Ensure that the main bar is in a different table row that is below your banner. I'm looking at this from work so half the time graphics don't load and I don't see your banner to really see the issue.
2) How can I remove Upcoming Raids? I don’t see it under ‘Menu Administration’.
Again for this you need to edit your layout.html file. You need to locate and remove the following tags.
<!-- System:NextEventName -->
<!-- System:NextEventDate -->
3) How do I limit the shouts listed?
Find this in the CSS editor. If it isn't there add it. overflow:auto specifically makes the box scrollable rather than show all. height:200px is the height of the box in pixels.
/* This is the Shoutbox style */
.shoutbox{
overflow:auto;
height: 200px;
font-weight:normal;
font-size: 7.5pt;
}