Step 1: Understand complexometric titration.
Complexometric titration involves formation of a stable complex between a metal ion and a complexing agentHere, Ni$^{2+}$ reacts with EDTA under basic conditions
Step 2: Role of EDTA.
EDTA is a hexadentate ligandIt binds metal ions strongly through nitrogen and oxygen donor atoms
Step 3: Stoichiometry of Ni$^{2+}$ and EDTA.
Most metal ions form 1:1 complexes with EDTA, irrespective of metal chargeFor nickel:
\[
\text{Ni}^{2+} + \text{EDTA}^{4-} \rightarrow [\text{Ni(EDTA)}]^{2-}
\]
Step 4: Check statement (B).
Since nickel and EDTA form a 1:1 complex, statement (B) is correct
Step 5: Role of indicator.
In complexometric titration, the indicator first forms a weak coloured complex with metal ionAt the end point, EDTA displaces the indicator from this complex
Step 6: Compare binding constants.
For a sharp end point, the metal-EDTA complex must be more stable than the metal-indicator complexTherefore, the binding constant of Ni-EDTA complex must be higher
Step 7: Conclusion.
Phenolphthalein is an acid-base indicator, not the suitable metallochromic indicator for this titrationAlso, EDTA does not form a 1:3 complex with Ni$^{2+}$Hence, correct statements are (B) and (C)
\[
\boxed{\text{(B) and (C)}}
\]