The problem is that, in the namelist.input file, I don't get the values for the e_we or e_sn for the two child levels; I only get them for the parent. Of course, I can figure out those values from the Domain Wizard, but I'm just wondering if it means I've done something wrong or that I could have problems in the future.
I am not sure, I understand your question, but you have to specify the grid specifications (including e_we and e_sn) yourself for all your grids. geogrid.exe won't provide that for you. It needs some time and thinking, to get the all the grids consistent and correct. Domain Wizard is a tool that can help you with it.
Also, should I treat the intermediate level like a parent or a child? I assume I should treat it like a parent.
It is both: It is the child of the coarser level and it is the parent of the next finer resolution levels.
To get an clearer idea about these concepts, these slides might help.http://www.mmm.ucar.edu/wrf/users/tutor ... esting.pdf