The Gromble was definitely male. His voice was often deep (and the scariest voice on the show when it was), but would often fluctuate between a deep voice, a high voice, and ranges in between. This was usually used for comedic effect. It was also one of the character's ways to scare his students as he would lore them into a false sense of security with an unthreatening and happy sounding high voice then suddenly the voice would get deep and you knew you were in trouble.
As for the shoes, only the show's creators know for sure but I think they used his high heels as a way to make the character a little less threatening and a little less scary. It was a kids show, after all, but the character was arguably the scariest monster on the show (and rightfully so as his job was to teach his students how to scare), but would have most likely been a little too much for some viewers so they wanted to add something that kids couldn't help but laugh at when they saw him, and they went with heels. The Gromble even had a strange obsession with his high heels as he had a closet full of them (much like a stereotypical woman would), and would, at least on one occasion, punish his students by making them polish them all.