These mechanized squads were intended to work in conjunction with tank forces in a similar to vein to the US Army's Armored Infantry.
Half-track-mounted mechanized infantry were actually the minority of Panzergrenadiers with most being motorized in trucks. In 1944, Panzergrenadier Divisions had 6 motorized Panzergrenadier Battalions and no mechanized. In Panzer Divisions, only 1 out of 4 Panzergrenadier Battalions were mechanized, the rest being motorized.
The Panzergrenadier Group differed from the standard infantry group in that it had 2 machine guns. This allowed the group to employ leapfrog fire and maneuver whereby one lMG Trupp covered another while it bounded. The squad would also have one Panzershrek rocket launcher and the machine gun mounted on its half-track manned by the Co-Driver at its disposal.
Also, til July 1944 the Deputy Group Leader was officially an NCO, implying a more involved leadership role in squad maneuvers. He was authorized a G41 self-loading rifle, although this could have actually been any rifle with an optic sight including the Kar98k and later G43 (this was officially the case after July 1944 and by Nov. 1944 the Deputy was no longer distinguishes from other riflemen and a dedicated Sharpshooter was added).
The Assistant Machine Gunners remained only pistol armed until July 1944 when they got rifles. Although the regular infantry did this back in 1943, keep in mind the Panzergrenadiers were in the Panzer troops rather than the infantry with their own distinct doctrine.