If my opponent KO'd one of my Pokemon and then on my next turn I use Origin Forme Dialga VSTAR's "Star Chronos" attack, or if I KO one of my opponent's Pokemon with Medicham V's "Yoga Loop" attack, can I play Raihan on the second of my two turns from either of those attacks?
Yes, you can. Your Pokemon was KO'd "during your opponent's last turn" regardless of how many turns you take since then.
Star ChronosYoga LoopRaihan