What is the difference here between مُدَرِّس and معلمة ?Also what does the root of هعلم mean?
I'm not sure of the difference, I'll leave it to an native speaker. But the root of معلم is ع ل م or 3-L-M, which has a basic meaning of "know" or "knowledge". Mu3allim / معلم means a person who causes someone else to know, so, a teacher. The mu- is actually a prefix that goes with this form.