Step 1: Analysing statement A.
$\mathrm{NH_3}$ has a higher dipole moment than $\mathrm{NF_3}$ due to stronger N–H bond polarity and vector addition. Hence, statement A is false.
Step 2: Analysing statement B.
$\mathrm{BeH_2}$ is linear and symmetrical, so its dipole moments cancel out. Hence, dipole moment is zero. Statement B is true.
Step 3: Analysing statement C.
Bond order of $\mathrm{O_2^{2-}}$ is 1 and bond order of $\mathrm{F_2}$ is also 1. Hence, statement C is true.
Step 4: Analysing statement D.
In ozone $(\mathrm{O_3})$, the central oxygen atom has a formal charge of $-1$. Hence, statement D is true.
Step 5: Analysing statement E.
$\mathrm{NO_2}$ is an odd-electron molecule and does not satisfy the octet rule. Hence, statement E is false.
Step 6: Final conclusion.
Correct statements are B, C and D only, corresponding to option (3).