So PNR 1 is Australia-Singapore with 4 correct names and PNR 2 is Singapore-Frankfurt with 3 correct names and 1 incorrect name - is that correct?
Name corrections (3 letters or less or juxtaposed names generally) and name changes (complete change of name or anything over 3 letters) can generally only happen when the PNR only contains flights that are marketed AND operated by the ticketing carrier. That is, VA can only do a name correction or name change on VA marketed and operated flights.
Partner carrier prime flights or codeshares generally cannot be changed as a name change or name correction. This is a general rule across the board with all carriers. There are a few exceptions eg. QF and EK, but for the most part, it's a no for partner prime flights or codeshares.
For reference VA clearly states no name changes here in the international tab:
Velocity Reward Seat | Virgin Australia
For all intents and purposes, consultant error or not, it's a name change that this person is needing. What is worse is it's the surname that's outright wrong. You're arguing semantics here and it does nothing to help the issue.
Absolutely. Airlines have no real obligation that they must carry a passenger with incorrect or invalid documentation. It would be up to the travelling party to decide how they wish to proceed, eg. one adult remains behind and the others travel, or everyone doesn't travel. It happens all the time on a daily basis. An airline is not going to risk a fine/ban/punishment from a government for carrying a passenger that doesn't meet all documentation requirements.