The search box is coming from your Genesis Theme settings. Go into your Genesis Theme settings and uncheck the box under the Primary Nav that says – “Enable Extras on Right Side?”
…The nav was designed/coded to be vertical for this theme, so I don’t have any extra “shortcuts” for it since that was the intention. However, you may be able to get away with removing the “clear: both” for the <li> – .menu-primary li, .menu-secondary li, #header .menu li on line 313
