Statement (A): Excessive shear reinforcement increases the confinement of concrete and forces the beam to fail by crushing of concrete (compression failure) rather than shear cracking. Hence, this is TRUE.
Statement (B): If no shear reinforcement is provided, beams may suddenly fail in shear even when they are safe in flexure. This leads to a brittle failure without warning. Hence, this is TRUE.
Statement (C): The longitudinal reinforcement does play a role in shear resistance. It contributes through dowel action across cracks, enhancing shear strength. So, saying it plays no role is FALSE.
Statement (D): According to IS 456:2000, the nominal shear stress depends on the design shear force $V_u$ and the effective depth $d$ of the beam. For varying depth beams, both the shear force and bending moment influence the shear stress distribution. Hence, this is TRUE.
Conclusion: Statements (A), (B), and (D) are correct.
\[
\boxed{\text{Correct Statements: (A), (B), and (D)}}
\]