Light reaction

Photolysis (splitting) of water is associated with photosystem II, on the inner side of the thylakoid membrane: $2H_2O \rightarrow 4H^+ + O_2 + 4e^-$
The electrons released replace those removed from PS II; oxygen is evolved as a by-product.
The oxygen-evolving complex contains manganese; manganese (with chloride ions) is needed for the splitting of water to liberate oxygen during photosynthesis.
Copper is a component of plastocyanin, boron is needed for pollen germination and membrane function, and zinc activates carboxylases and is needed for auxin synthesis.
Hence manganese is essential for photolysis of water.

(A) is wrong: the Z scheme (non-cyclic electron flow) needs both photosystems, PS II first and then PS I, connected through the electron transport chain.
(B) is correct: when only PS I is functional, the electron is circulated within the photosystem and cyclic photophosphorylation occurs.
(C) is wrong: cyclic photophosphorylation results only in the synthesis of ATP; $NADPH + H^+$ is not formed.
(D) is correct: the stroma lamellae membranes lack PS II as well as the enzyme NADP reductase; this is where cyclic photophosphorylation takes place.
Hence the correct statements are B and D.

In cyclic photophosphorylation only PS I is functional; it occurs in the stroma lamellae, which lack PS II and NADP reductase.
The electron excited from P700 is not passed to $NADP^+$; it is cycled back to the PS I complex through the electron transport chain.
This cyclic flow results only in the synthesis of ATP.
NADPH + $H^+$ is not formed, and since PS II is not involved there is no splitting of water and no release of oxygen.
Hence cyclic photophosphorylation results in the formation of ATP only.