Is there any way to add a headline above the text? In a heading font?

Sure. You could use :before instead of :after. You would also want to use a different selector depending on exactly what text you want to place the headline before. Here are a few examples to get you started.

This will add large, bold text above the recent articles section:

.home .section-title:before {
	content: "Example Headline";
	font-weight: bold;
	font-size: 20px;
}

This will add a headline before the recent articles articles section styled in the same way the recent articles heading appears. I did this by copying the CSS used for ".section-title h1" by the theme. I found the CSS by right-clicking the recent titles heading and selecting the "Inspect Element" option.

.home .section-title:before {
	content: "Example Headline";
	display: block;
	background: #F3F3F3;
	border-left: 10px solid #E9E9E9;
	color: #999;
	font-size: 1.3em;
	line-height: 1.7em;
	margin-bottom: 20px;
	padding: .25em .6em .3em .6em;
	text-transform: lowercase;
	width: 94.5%;
}

You can try out these examples and adjust them until the heading looks good to you.

.home #content-wrap:after {
	content: "Replace this with the tect you'd like to add."
}

Thank you so much for your help!

Hopefully the MonsterID option will workout for you instead!

I would like it to point to:
"http://gravatar.com/anonamonster" instead.

Now just need to understand how to do it - the hard part. :)

First of all, thanks for the response. The link you provided was very informative. Unfortunately, it seems either too generic (or more likely) too advanced for my current level of css skill.

I was able to "inspect element" of the "anonymous" name via chrome. Here's what I came up with:
<div class="author">Anonymous</div>

I'm sure this is what I need to edit, change, or modify. Your link may have helped a more html savvy person figure this out, but I'm still a bit lost. Any more assistance in narrowing down how to change this element would be much appreciated.

The MonsterID is a great backup if I can't figure out to pick a specific icon for anonymous users. There's got to be a way to insert an image though . . . once I figure out what specific element I'm trying to modify and how to change it the way I want.

Trying to change the username of all anonymous users to "Anonymonster" instead of "Anonymous."

CSS has a property named "content" and you can combine it with psuedo elements to add text before or after existing text. Here is the documentation for how it works:
http://www.w3.org/TR/CSS21/generate.html#content

I would also be interested if it would be possible to set up a specific icon for those anonymous users.

There is a built in option to change the default avatar to a generated version, and there's even one called MonsterID there. Would that work? To find it, go to Settings → Discussion → Avatars → Default Avatar.

I would also be interested if it would be possible to set up a specific icon for those anonymous users.

Any assistance would be greatly appreciated