To something that I like maybe with my logo appearing in the middle?

If you still need help with this, could you point out exactly where you're trying to add your logo in the middle?

3. How do you personalize the line that appears under each posting?

You could do this using the content property. Here is an example of adding text:

.post-meta:before {
	content: "Replace this text.";
}

To add text and an image, you could start with something like this and adjust it:

.post-meta:before {
	background: url(http://s.wordpress.org/about/images/logos/wordpress-logo-32-blue.png) no-repeat;
	display: block;
	min-height: 32px;
	padding-left: 40px;
	content: "Replace this text.";
}

Replace the url() value with your image and update the min-height and padding-left values to your image dimensions.

The examples above will work on archives pages (pages that list posts). The Mystique theme adds in a special author section below the content on individual posts automatically. To adjust the image there, update the post author's Gravatar. To adjust the text, edit the Users → My Profile → About you setting in your blog dashboard.

2. I want to add my own social networking icons on the top page of the site. How to do that with CSS?

What you can do is add them into your sidebar using a text widget, and then you can move that text widget to somewhere else on the page using CSS.

p.author { display: none; }

2 & 3 are beyond the scope of CSS really.

I am busy figuring out the layout of the site before I make everything final. I need help with CSS coding as I am stumped.
1. How to remove the "Posted by....." which is found next to the date when you add a new post. I know how to fully remove it but it takes out the bar and looks funny because its not adjusted to the date image (little bit of he bar left attached to the date image). I just want to remove the text and not the entire bar (section its written on)
2. I want to add my own social networking icons on the top page of the site. How to do that with CSS?
3. How do you personalize the line that appears under each posting? To something that I like maybe with my logo appearing in the middle?

I am using Mystique theme. Help!!

Thanks!

.post .post-info {
    display: none;
}

.entry-meta {
display: none;
}

Also on CSS related questions, please post in the CSS forum as that is where I look first for CSS related questions and you will likely get a quicker response. Thanks.

Which CSS code do I have to create - and copy/past - into the CSS Stylesheet Editor?

The other choice would be to set yourself up a test blog to play with on your existing account which you could keep set to private.

You can also add the authors widget to the sidebar and then when someone clicks on one of the authors, they will get a listing of only the posts by that author.