Relating to Chrono Cross, I don't play that game because the battle system is too weird and confusing for my taste, and I don't think it count as a "true" sequel to Chrono Trigger anyway. Originally the game was titled Radical Dreamers and did not contain any reference to Chrono Trigger.

About TMNT, that always confused me, too. The game does this so you can regain a captured Turtle. But the only explanation I can come up with is that the "demutation" is temporary and the Turtle "remutates" shortly afterward. As for not killing them outright, perhaps they are under orders from Shredder to leave them alive so he can execute them himself later.

Another one is common in many platform games, but especially in the Mario series. Almost all Mario games contain underwater levels which Mario can swim through (and does not appear to have any need for air, but let's not go there just yet). In other levels there is only surface water, which will instantly kill Mario if he falls into it. Why can he swim in some levels and not in others?