This is true for most cases. However, exceptions exist:
- Male: Der Arzt; Die Ärzte (pl)
- Female: Die Ärztin; Die Ärztinnen (pl)
- Male: Der Soldat; Die Soldaten (pl)
- Female: Die Soldatin; Die Soldatinnen (pl)
There are more, but these are all I can remember right now.
Well the German for the verb 'to haggle' is 'feilschen', but I'm not 100% about the word for 'haggler'. But 'Handler' (yes, yes, I know, there's no umlaut) means generally: trader, dealer (including cars etc), store owner and such words as 'Fischhandler', Fleischhandler, Gemusehandler, well you get the drift. Again, no umlauts as I have to add them from another place for now, and it's inconvenient.