[Godslayer Jillian]

At first, I didn't like your post, but you proved you can be quite articulate, and you do know how to get to the point reasonably.
Anyway, let's see.
In the beginning, the point of Goth was basically the same as Punk, but less agressive. Basically, where punks would anger on what they don't like, goths would mourn on what they don't like, but not on a "Woe is me" way.
On fashion. You would have to tell us what kind of "goths" you have seen. If you see a guy with terribly smeared make-up, styled as The Crow, with baggy chain pants, and/or T-shirts of bands that only scream; feel free, nay! feel encouraged to mock them.
My kind of style is Victorian (and Edwardian).
Coats, cassocks, silk shirts, vests... that's my preferred way to go.
The other "gothicky" fashion style I like is the deathrocker.

On music.
It's not about pain and suffering. Indeed, many have dark themes (I mean, come on; a kid can see that goth IS dark) like death, or solitude, but look at the difference:

- "Slit my throat, for I don't want to be a part of life. No one cares, no one listens, no one gives a..."

-"Is there really so much egoism in the world? Is there really so much self-obsession that love nolonger counts? Isn't it enough that everyone is out for themselves and no-one understands That the walls of solitude are the walls of egoism? (Fassade III, by Tilo Wolff; not entirely goth, but an example that is melancholic)

I would really reccomend for you to look for some traditional gothic music; particularly Siouxsie and the Banshees.
You will find Siouxsie's songs quite un-parallel to any presupposition you had of "gothic" music.

On cutting one's wrists:
I hate it!
I find it weak. I find any addiction weak.
I don't only hate "goths" that cut their wrists. I just don't like people that cut themselves, regardless of such a vanality as style.
But people showing off their wrists as a "dark" status symbol piss me off more than anything else. I see one and wish they had cut a little deeper.
So, no; cutting one's wrists is nowhere near goth. It's nowhere near emo either, but that term has been desecrated so long that if I said emos cut, it wouldn't be a stereotype; it would only be a generalization.