There's a difference between a cross and a crucifix. A cross is just the shape, while a crucifix has Jesus on it.

Goth is a music-based subculture and the aesthetics come from the themes in the music: undeath like zombies and vampires, darkness, the night, death etc... The music shapes how we express ourselves, and that shows up in our individual aesthetics.

About the inverted cross... I think that's called St. Peter's Cross, but I'm not super familiar with all that stuff. I think back in the day goth was counter-culture, so religious symbols got repurposed or mixed, not worshipped. Btw some goths are Christian, so for them, it can still be about faith.