X does not have the shortcodes that you mentioned as the archive pages you mentioned are using the file templates that you can override through a child theme, but this would be outside the scope of support we can offer. You may wish to consult a developer to assist you with this. X is quite extensible with child themes, so there are plenty of possibilities.
A workaround I could suggest would be to use some of the bundled plugins with X like The Grid and Essential Grid plugins which will allow you to display posts according to their category, and other filters.
Hope this helps.