To get your shop accessible from the root domain name, you will need to either do a redirect to /shop/ or move the installation from /shop/ to the root (/public_html/).
Many people do their development work in a subdomain like /shop/ so the unfinished site is not out for all the workd to see, and move it to the root when finished. This is not a complicated job; after moving all the files & folders, you just have to eliminate "shop/" from a dozen places in two files. There is a tutorial that gives full instructions.
Define_main_page.php controls the center column of the home page. To turn off the rest, you will need to edit /includes/templates/your_template/common/tpl_main_page.php. There are instructions at the top - essentially, you would add
if ($this_is_home_page) {
$flag_disable_header = true;
$flag_disable_footer = true;
$flag_disable_left = true;
$flag_disable_right = true;
}
```though you might want to leave at least part of the footer.
You can copy parts of the tpl_header.php code into your custom home page, like the logo and some links, and put them where you want them.