Is fellép related to fel+lép, as in stepping up somehow?
Yes, good catch. I can also offer you the German "auftreten", which has the same literal and figurative meanings. You can imagine it like stepping onto the stage/scene (szín in Hungarian, easy to remember).
I imagine that during the Hungarian language reformation in the 18th and 19th centuries, Hungarians formed many words from German calques.
I do not understand why "female" singer is still rejected. reported