user empties cart how do I redirect that user to originating page
In your first rule "Redirect to cart after adding a registration" you probably are using a "Page redirect" action. If so you can do the following.

Edit this action and set "APPEND DESTINATION PARAMETER" to true (see screenshot). 
This will add the referring page as a query parameter to your url e.g. example.com/cart?destination=node/3 

Then in your second rule you can retrieve this destination parameter by using the function drupal_get_destination. Use the return value of that function in the drupal_goto function and the user will be redirected to the url they were coming from.

{ "rules_redirect_user_to_originating_page_after_removing_all_items" : {
    "LABEL" : "Redirect user to originating page after removing all items from cart",
    "PLUGIN" : "reaction rule",
    "OWNER" : "rules",
    "TAGS" : [ "Cart" ],
    "REQUIRES" : [ "php", "rules", "commerce_cart" ],
    "ON" : { "commerce_cart_product_remove" : [] },
    "DO" : [
      { "php_eval" : { "code" : "drupal_goto (drupal_get_destination());" } }
    ]
  }
}