wp-21

Hi,
You are advised to use a child theme for any edits to save your data from loosing upon updating your theme in future.
Refer to this:
http://codex.wordpress.org/Child_Themes

You can find the header.php file from Appearence>>editor from your dashboard..

Cheers..:)..

Hi,
You can use conditional statements inside the header.php file of your child theme to display header image only on home page,like

<?php if(is_home) { ?>

  <div class="head-img">
  ...
  </div>
  <!-- END Header -->

<?php } ?>

or

You can use CSS to hide it on other pages via display:none property

Hi,
You can change it via CSS, pls post a link to your site for further help..

cheers..:)..

Hi,
Check this out:

http://slobodanmanic.com/444/flexible-horizontal-sidebars-wordpress-twenty-thirteen-child-theme/

Cheers..:)..

And regarding that space appearing in the other pages, It is due to margin applied on the p tag.

I see that you have placed the image first and aligned it to the right, but that image is being surrounded by p tag on which a margin top and bottom of 16px is being applied somewhere in your css.

You just need to reset the margin on p tag to ensure the space is removed on all of the pages.

Cheers..:)..

Hi,
The code should work, try using important!:

.header-widget {
    float: right;
    margin: 0 !important;
}

and no need of px when 0.
And for the space between the menu and the content reduce this argin to 0.

#main {
    margin-top: 40px;
}

Cheers..:)..

Hi,
From where did you place the header image..?
You can place this code inside header.php file.

<map name="header-stein-hawt">
    <area shape="rect" coords="275, 0, 645, 100" href="http://haveartwilltravel.org" title="Have Art: Will Travel! Inc." alt="Have Art: Will Travel! Inc." />
</map>

Cheers..:)..

Hi,
You have declared two font-sizes and in CSS the one which comes later is applied, So just comment the rem font-sizes or remove them.

Cheers..:)..