I’m not sure about step children, but I did light for one of my foster children. We thought he would be with us long-term & he did not have a mother so our rav told me to light. He ended up leaving us and I continued lighting (as we don’t reduce kedusha). When my next child was born we asked whether to add or just count that one for her (we do have a minhag to add for each child) and were told to add.
In terms of forgetting- I forgot once and the rav told me to add extra oil from then on. The reason it goes forever (and not just till Yom Kippur) is that it is not a punishment, but rather a reminder not to forget again.