Hi,
Regarding the shipping methods, your shipping methods seems to be setup properly. Please make sure that you have the shipping view in your checkout workflow in the configuration and that the auto selection shipping and payment methods option is turned on and that should help.
Regarding the Popup, instead of the code:
JHTML::_('behavior.modal');
echo _('<br />').JText::_('MANUFACTURER').': '.'<a class="modal" rel="{handler: \'iframe\', size: {x: 600, y: 350}}" href="'.hikashop_completeLink('category&task=listing&cid='.$manufacturer->category_id.'&name='.$alias.'&Itemid='.$Itemid).'" >'.$manufacturer->category_name.'</a>';
use the code:
JHTML::_('behavior.modal');
echo _('<br />').JText::_('MANUFACTURER').': '.'<a class="modal" rel="{handler: \'iframe\', size: {x: 600, y: 350}}" href="'.hikashop_completeLink('category&task=listing&cid='.$manufacturer->category_id.'&name='.$alias).'" >'.$manufacturer->category_name.'</a>';
and that will remove the ?Itemid=468 in the URL for the popup.