The widgets look untidy and clumped together how can I make it so they are neat?

It looks like you added a background color to one widget and the padding that was acting as a separator before now looks too close to the search widget above it. One possible way to solve that for your site would be to add extra padding below the search widget like this:

#search-2 {
	padding-bottom: 20px;
}

I'd like a Facebook badge but where so I insert the coding?

Check out this page for instructions:

http://en.support.wordpress.com/facebook-integration/facebook-badge/

Widgets for categories showing in grey text

You can adjust widget category link text color by adding this to your Appearance → Custom Design → CSS editor:

.widget_categories .cat-item {
	color: #000;
}

I look forward to hearing from you and thank you!
Blog url: http://assystem.wordpress.com/