batharoy

.widget_circleicon-widget {
    clear: none;
}

Will align the footer widgets horizontally in the footer.

It looks like you have 2 blank text widgets in your sidebar. You can remove them through Appearance > Widgets.

After doing more research on my local system it appears using a child-theme breaks the menu styling and functionality on this theme.

As you can see by the linked screen shot your cache/minify css still has the setting at 3px. When its unchecked in DevTools it does center the image.
You may have to clear the cache or wait longer for it to clear itself.
http://s28.postimg.org/81dawid19/Untitled.png

#site-logo > a > img {
    box-shadow: none;
}

You would want to use a custom css plugin or child-theme to make the edits. Any edits made to the original files will be overwritten if the theme is upgraded.

Then for the search just add 100% width.

#top-search {
    width: 100%;
}

@rpitts
Since your using a child-theme, it would be easy to add it to your header.php
Start by copying your header.php into the child-theme folder.
Then find your <hgroup> code and change to look like the following, changing the address & phone of course.

<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' ); ?><br />
ADDRESS<br />PHONE #</h2>
		</hgroup>

Then remove any styling you added to the <hgroup> and .site-description etc..
We can style that so it appears right aligned after these steps.