For 1 you need to move:
<?php if ( get_header_image() ) : ?>
<a href="<?php echo esc_url( home_url( '/' ) ); ?>"><img src="<?php header_image(); ?>" class="header-image" width="<?php echo get_custom_header()->width; ?>" height="<?php echo get_custom_header()->height; ?>" alt="" /></a>
<?php endif; ?>
above the <nav>
tag in the header.php
file.
For #2 you need to increase the .site-header h1
font-size
to a higher number.
For #3 you need to change the colour to: color: #084b8a;
EDIT:
<header id="masthead" class="site-header" role="banner">
<hgroup>
<h1 class="site-title"><a href="<?php echo esc_url( home_url( '/' ) ); ?>" title="<?php echo esc_attr( get_bloginfo( 'name', 'display' ) ); ?>" rel="home"><?php bloginfo( 'name' ); ?></a></h1>
<h2 class="site-description"><?php bloginfo( 'description' ); ?></h2>
</hgroup>
<?php if ( get_header_image() ) : ?>
<a href="<?php echo esc_url( home_url( '/' ) ); ?>"><img src="<?php header_image(); ?>" class="header-image" width="<?php echo get_custom_header()->width; ?>" height="<?php echo get_custom_header()->height; ?>" alt="" /></a>
<?php endif; ?>
<nav id="site-navigation" class="main-navigation" role="navigation">
<h3 class="menu-toggle"><?php _e( 'Menu', 'twentytwelve' ); ?></h3>
<a class="assistive-text" href="#content" title="<?php esc_attr_e( 'Skip to content', 'twentytwelve' ); ?>"><?php _e( 'Skip to content', 'twentytwelve' ); ?></a>
<?php wp_nav_menu( array( 'theme_location' => 'primary', 'menu_class' => 'nav-menu' ) ); ?>
</nav><!-- #site-navigation -->
</header>
ANOTHER EDIT:
<?php if(is_front_page()) :
echo '<img src="">';
endif; ?>