I hear that it is a problem to step over a child who is on the ground, and that the person should go back if he did. Is that true halachically? Or is there an inyan not to do so?
It is definitely not a halacha, however it seems that this is a minhag among many people. The source of this minhag is not known, it is one of those things that “the ladies” have been saying for generations, and this is what many people hear from their mothers etc. The Be’er Moshe 8-36 says that this is one of those minhagim that would be included in what the Rashba said, that a person should not be mezalzel with the minhagim of the old ladies, because they surely have solid sources, even though we don’t know their reason.
Be’er Moshe 8-36, Mishneh Halachos 13-119, Selas Rav 1-chap. 21-8.