State the site of the light reaction and dark reaction in photosynthesis,respectively.

For the synthesis of one molecule of hexose,how many additional molecules of $ATP$ are required in $C_3$ and $C_4$ pathways,respectively,besides the $12$ molecules of $NADPH_2$?

$A-$ In chloroplast,the membrane system is responsible for trapping the light energy and also for the synthesis of $ATP$ and $NADPH$. This is called the light reaction.
$R-$ In the stroma,enzymatic reactions incorporate $CO_2$ into the plant,leading to the synthesis of sugar.

Provide the full names for the following abbreviations:
$(1)$ $NADP$
$(2)$ $ATP$

Provide definitions/explanations for the following terms:
$(1)$ Dark reaction
$(2)$ Photophosphorylation

Select the correct option for $NADP$ reductase.