Well,you gotta watch out for those stepfathers.Usually,how far he can go is decided by the mother,but in my opinion,kids always get the short end when mother remarries. I knew one family around here;the mother remarried,then she died of cancer and the stepfather charged her kids rent to live in their own house.
yes if they need punished for something that they knew was wrong. If we are not punished once in a while then if we do something wrong we think, "well nothing bad happened the first time, i guess it is okay to do it again" Thats just how our minds work. And a stepfather still has the authority in the house so yes i believe he can.