No, the real Olivia is pretty clear that she was hit by her mom. There's a Conan interview where the poor host is all "but you don't mean real hitting, do you?" And she cheerfully confirms that yeah, that's what she means.

If she was mocking or making light of that as an outsider, it would definitely be wrong! But as someone who's been through it, she has the right to react to her own experiences however she wants. (Up to a point, obviously! If she went on to hit kids of her own, that would be bad. But as it is, she hasn't done anything I'm going to judge.)

Will fix the typo!

Steve has a part in the crossover episode, yes. It's to promote the movie, and he was in the movie, so they brought him along.