You put the social icons inside paragraph <p> and that's why it has margins. So, you should remove <p> and ending </p>
Background color of the buttons is in file template_css.css around line 652. You should change color values for #nav > li. If you want plain pink color, you can just remove this part:
Code:
/* IE9 SVG, needs conditional override of 'filter' to 'none' */
background: url(data:image/svg+xml;base64,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);
background: -moz-linear-gradient(top, rgba(0,0,0,0.32) 0%, rgba(0,0,0,0) 100%); /* FF3.6+ */
background: -webkit-gradient(linear, left top, left bottom, color-stop(0%,rgba(0,0,0,0.32)), color-stop(100%,rgba(0,0,0,0))); /* Chrome,Safari4+ */
background: -webkit-linear-gradient(top, rgba(0,0,0,0.32) 0%,rgba(0,0,0,0) 100%); /* Chrome10+,Safari5.1+ */
background: -o-linear-gradient(top, rgba(0,0,0,0.32) 0%,rgba(0,0,0,0) 100%); /* Opera 11.10+ */
background: -ms-linear-gradient(top, rgba(0,0,0,0.32) 0%,rgba(0,0,0,0) 100%); /* IE10+ */
background: linear-gradient(top, rgba(0,0,0,0.32) 0%,rgba(0,0,0,0) 100%); /* W3C */
filter: progid:DXImageTransform.Microsoft.gradient( startColorstr='#52000000', endColorstr='#00000000',GradientType=0 ); /* IE6-8 */
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