Nope. As far as I'm aware, neither Shelmet nor Accelgor is available through the Dreamworld. That said, a few sites I've been looking at (Serebii, Bulbapedia) say that Accelgor's Unburden ability is available. It may be a similar thing to Musharna; that one's Dreamworld ability is available only because it is available on Fridays in a secret part of the Dreamyard in the game itself. It might be a similar thing with Accelgor.
Now onto your other questions:
1) go to http://www.pokemon.com/ and register an account. Have you done? If so go to http://pokemon-gl.com and put in the username and password you chose at the official pokemon website. Now you get to choose a different name to be known by there.
It's to do with security; no-one who interacts with you in the Dreamworld will be able to tell your sign-in name there, so they won't be able to hack you.
So, done? Right, now it's time to register a game card with the Dreamworld. The site will ask for a Game Sync ID when you first log in, or ask to register a Game Card, so pull up your DS, put in your Black or White gamecard and get to the bit where it asks if you want to get a Mystery Gift, continue, and so on. Don't continue yet; you want one of the options here.
Go down to 'Game Sync Settings' on the Mystery Gift, New game, etc. list and the game will ask if you want to connect to Nintendo Wi-Fi connection. Choose 'yes', and wait a while. When the number comes up, copy it into the Game Sync ID box on your computer browser.
Now you're on the Dream World.
Question 2: No. If you breed a Dreamworld pokemon with a DITTO you LOSE the ability. If you breed a MALE Dreamworld pokemon with ANYTHING, you lose the ability. Only FEMALES can PASS ON ABILITIES, but NOT WITH A DITTO.
Yes, yes. Caps make it look like I'm shouting, but I don't know what type of code this thing takes to accentuate writing. I'm not even sure whether I can edit, since I came on specifically to answer this.
On to question 3: The most useful thing the Dreamworld lets you do is access Berries. Wanna reset your Uber pokemon's stats so you can use the Effort Values elsewhere? Find the requisite Berry, plant lots, water them, then transfer them to your game with Game Sync. They'll turn up at the entralink.
Want a Poison Recover Gliscor for a really mean team member? Find it in the Dreamworld by playing a minigame, and send it to your game by making a wish at the tree. It'll turn up at the Entralink when you use Game Sync.
Want items and stuff you can't find anywhere else?
Well, you get the idea.