Hi Ray,
The search bar/social icons are all done in the header.php. So for
1. You can remove/move the code for the social media icons in the header.php file, look for:
<ul class="social_bookmarks">
Just make sure to take the entire ul all the way down to the comment "end social_bookmarks".
2. You can create your own icon by adding in the code into that ul and then into your css file. So you'll need to add something like:
<li class='gplus'><a class='ie6fix' href="http://yourgooglepluslink">Google+</a></li>
Then add the css and icon link to your style.css file:
.social_bookmarks .gplus a{background: transparent url(url for where your icon is) 0 0 no-repeat;}
3. This one is a bit more complicated. It would probably be easiest to look for a plugin to handle adding this in than to go through and manually add the code to the theme files.
Regards,
Devin