Why don't you show me a video of either scenario happening, first? Didn't happen to save the replays, did you?
Oh well, doesn't matter. I'd probably use it to criticize the mistakes made by either you or your team.
The first sounds like an assassin properly planning a gank in bot lane. Between the time to walk to bot lane and her passive's CD reduction, it's not surprising that she could pull off a double kill, especially if she teamed up with her jungler on that gank. You didn't make any mistakes, except for possibly not calling MIA; bot lane should have wards to watch out for ganks.
The second sounds like she jumped on a target who was about to die regardless of her ultimate, because there's no way that having the vast majority of her kit's damage negated didn't affect her. She just chose to jump on someone who was overextended for their low HP. Again, not your fault, as you were apparently playing Kassadin, who does not have the means to shove an assassin off of vulnerable allies.
Without an actual replay, the best I can say is that it's not your fault, and there was nothing you could have done in either of those situations aside from playing an entirely different champion. So long as you didn't feed Katarina, the problem is more likely your teammates' mistakes.