Validating subset of a password
Validating individual letters of a password reduces complexity of guessing that password by trying all possible variants, so I would suggest avoiding such a design.

PCP (probabilistic checkable proofs) is a well-known case of validating just a small portion of the "witness" (defined in that context), with focus on algorithm complexity.

Regarding "1st Edit": pass/fail response to "simplified" query is exactly how complexity is reduced. Random selection of letters requested might be considered a challenge/response scheme, on condition it can not be affected. Worst case would be repeated or single-letter queries.