The very final latest versions had 13mm guns on them, yes. Most had 1x7mm in nose, 1x7mm in dorsal, 1x7mm ventral bin firing aft, and the 20mm (if equipped) was in ventral firing fore/down. There were side guns equipped in a window on each side, but often these were of little use and many were removed in the field.
As for the payload: The He111 could carry larger over-load bombs, but only 2 of them on an external rack. Unlike the Ju88, which could carry external AND internal, the He111 could only carry one or the other, as the external rack mount blocked the bomb bay doors completely.