Check (A).
Ustad Mansur flourished in Jahangir’s atelier and is celebrated for exquisitely naturalistic studies of birds, animals and plants \(⇒\) True.
Check (B).
“Jahangir Weighing Prince Khurram” is a well-known Mughal work commonly attributed to Manohar (Manohar Das) from the imperial studio \(⇒\) True.
Check (C).
Govardhan worked under Akbar, Jahangir, and Shah Jahan and contributed to illustrated manuscripts including the Baburnama \(⇒\) True.
Check (D).
Nainsukh was an 18th-century Pahari painter (Jasrota/Guler circle), not an Aurangzeb-era Mughal court painter; famous for portraits of Raja Balwant Singh, not Aurangzeb \(⇒\) False.
\[
\therefore \text{The true statements are } \boxed{(A),(B),(C)}.
\]