You can confuse them by asking them if they know of the effects of sideslip on the low speed power required - evidently the Canadian CH-46 SAR model had a sideslip indication for single engine fly-away to get better performance.
As for the other stuff - very complex, and I'm surprised that anyone would be asking those sort of questions. My answers would be:
interference effects on induced power - there may be some interference effects on power required overall, but you would have a difficult time to separate induced power from the total power
LCT and parasite power - how do you separate this out? - the LCTs might (and even that is a bit of a stretch) effect things slightly at extremes of CG, but you as the pilot have no real control over them. Parasite power, (at least in my books) is for things like transmission losses, hydraulic pumps - how does this relate to LCT?
Tandem rotor and profile power - a bit of a red herring (unless my understanding is way off) - the lack of a tail rotor only means that all the power can go to vertical thrust. Profile power is the power to just turn the rotors, so while a tail rotor may take less power to turn than a main rotor, it's not really contributing to lifting stuff...
Just my two cents worth.