Adding a divider line and space between homepage posts

In your stylesheet, change this:

#content h2 {
    font-size:27px;
    margin:5px 0 7px 0;
}

To something like:

#content h2 {
    font-size: 27px;
    margin: 50px 0 20px 0;
    padding-top: 10px;
    border-top: 1px solid #666666;
}

Adjust the padding, margin, and border colours/thickeness as you like.

Just watch out: use a custom stylesheet if your theme offers one, or build a child theme – otherwise beware as your style tweaks will likely be overwritten if you update the theme in future.