More header questions

Trying to get a header image to display without top, left, or bottom margins, but still with search/social icons.

When viewed in IE, this is the look I’m going for, but it doesn’t render nicely on mobile. Any help?

http://www.diprecipecreations.com/recipes/

Child theme CSS

#site-title {
margin:0;
line-height:0;
float:left;
}

#header {
border-top:#2d2006 0px solid;
}

#header #searchform {
float:right;
margin:59px 3.4% 0 3px;
}

#social-media-icons {
float: right;
margin-top: 59px;
}