Who first demonstrated the $C_4$ pathway?

Some of these terms/chemicals are associated with the $C_{4}$ cycle. Explain.
$(a)$ Hatch-Slack pathway
$(b)$ Calvin cycle
$(c)$ $PEP$ carboxylase
$(d)$ Bundle sheath cells

$C_4$ plants are found among

$C_4$ plants are more photosynthetically efficient than $C_3$ plants because:

Assertion : $Amaranthus$ and sugarcane are called as Hatch and Slack plants.
Reason : One glucose is formed by fixation of $6 \,CO_2$ in the plants.

In $C_4$ plants,the bundle sheath cells