Like already said before: Wikipedia describes it quite well, including most known bands for every genre:
http://en.wikipedia.org/wiki/Heavy_metal_musicNot on your list but hilarious: Doom metal. Not to listen to, but live. "Now, it's time for a fast song."
Priceless. Should call it Snail Metal or something though. Or snooze metal.. or I-only-had-1-minute-of-material-and-smeared-it-over-a-whole-concert-metal.
Speedmetal: Can't be accused for being slow. Running Wild describe themselves as speedmetal. (they sing about pirates! how neat is that!) Not sure if Peter Pan Speedrock falls into that category. it has 'speedrock' in the name, close enough. Can't name other speedmetal bands at the top of my head.
Rock 'n roll's definition has been evolved quite alot overtime. See wiki. Even the Osmond siblings used the words rock 'n roll!
Headbanger. Someone who headbangs, headbanging is the fine art of tossing your head with long manes around. either up and down (I once joked 'metalheads aren't rebel at all, they always nod yes' and noone laughed.. I think it's funny!), or completely around. you can shake your head. Or if you're weird like me, make triangles. See wiki on Headbanging. Don't take everything serious though. Not every metalhead wears shitty green jackets, though a huge patch of your favourite band on the back is quite common. It's fun to examine all the patches of an avid metalhead's jacket and see how many bands you know. Best place: metal festivals. You can even hear some nice stories of the older guys.
Punk. No idea, actually, it only just reminds me of Vyvyan of The Young Ones and Sexpistols (God save the Queeeeeen!). that's all I know. Also, that Gothic is originally branched off from punk and is very electronic, lessay Sisters of Mercy. I'll pass this question.
I am guessing alternative music is also nicely described in the wiki. Everything small, independant and undergroundy. Though when I was 15-18 though, it would probally be a pleonasm because punk=alternative. rock/metal=alternative. and scary.. Then again, everyone with a bit too many black accessoiries was swiftly called an 'alto' (a Dutch term) at my school.
If you plan on writing a paper for school, I suggest looking in your local library for books about music. I'd be viciously murdered if I tried to write a paper using only wikipedia for example..