Remove lines above and below header image?

I’d also like to get rid of those bullets in the nav bar.

Try adding this in your style.css (main style file)

.menu-contact-container ul {
    list-style:none;
    margin-left: 10px;
}

Also locate this code:

#branding img {
border-top: 4px solid black;
border-bottom: 1px solid black;
display: block;
float: left;
}

Just remove the two lines specifying the border.

To remove the bullets, I did this:

.menu {list-style:none;}