Testing PRNG quality from ECC public keys? Having a large set of ECC public keys $P_i = n_iB$ on a fixed curve $E$ over a prime field, is there a way to determine if coefficients $n_i$ were generated using a bad PRNG?

In other words, can a quality of PRNG be tested by knowning the ECC public keys?
No, not in general without a model for how the PRNG might be bad.  If the PRNG is bad, then there is a test to distinguish it from (say) uniform random bit string outputs; you must then adapt that test to work not on bit string outputs, but on the resulting curve points.  How you do this depends entirely on how the PRNG is bad.