assign specific products to a specific menu

Hi,

It's normal. If you add manually the cid parameter in the URL, the cid overrides the category selected in the menu item options. That's how you can navigate from the categories listing to the products listing of one of the categories of the categories listing by adding the cid parameter in the URL.
But if you create menu items with different categories selected in them, that's not the URLs you will get in your menus module.
You'll get these URLs:
index.php?option=com_hikashop&ctrl=category&task=listing&Itemid=142
index.php?option=com_hikashop&ctrl=category&task=listing&Itemid=143
index.php?option=com_hikashop&ctrl=category&task=listing&Itemid=144
And these will display the listing based on the category selected in the menu item options.

I don't see why you wouldn't want the URLs that you put in your message to do what they do.
Maybe I don't understand your issue, or maybe you have a reason I don't know in wanting to do that.

Could you provide a link to the shop so that we could see exactly what you did and explain what you want to change exactly on which pages ?