Grey vertical line in header

That line is coming from the border-left defined here:

.main-navigation {
  border-left: 1px solid #cccccc;
  display: block;
  float: right;
  font-family: "Open Sans Condensed", Helvetica, Arial, sans-serif;
  font-weight: bold;
  max-width: 50%;
  position: relative;
  text-align: right;
  text-transform: uppercase;
}

To remove it, add this to your custom CSS:

.main-navigation {
  border-left: none;
}