The mapping file will need the site URL updated if that is now different, yes. If the column names have changed, the mapping would also need to be updated.
If an XML has values in the field mapped to the SharePoint list ID, qRules is going to try to update the existing item - so if your form has, for example, an item with an ID of "420" and there is no item with that ID in the list any longer, the code can't know what item it should update. Does your list have items in it? Maybe there would be a way via form logic to update the ID field in the form to the correct new ID?