How to remove header for all pages to reduce space in between? - see attached
I suggest you check firebug tool in firefox to inspect CSS and HTML.
I figured this one - in style.css, search for 'heading1' and add last line as 'display: none;'
also add ; after 34px
.heading1 {
margin-bottom: 20px;
border-bottom: 1px solid #efefef;
margin-top: 0;
font-size: 34px;
display: none;
}