To answer your questions -
1. Yes and no. Your real name can be your business name. If you pick a business name, you will have to get a bank account with that name, because people will want to write checks. It doesn't cost anything. You just tell your state IRS that you need a tax id number (if your state has sales tax). Whenever you sell to someone in your state, you need to add on the tax, and then pass that on to your state IRS at regular intervals (they will tell you)
2. You have to set up a booth at home the way it would look at a craft fair. Take a picture of it and send it to them. they want to make sure your booth is classy enough for their fair. An excellent publication with advice is http://craftsreport.com
3. I started with a freebie site at Geocities.com and then upgraded to paid when the money started coming in. You can pick a template and then just plug your stuff in. So it was free at first, then, since I was leaving Geocities, I paid $75.00 for web design software, and now I pay $7.00 a month plus $9.00 a year for my dot com name.
4. I get the names of shows from the newspaper websites. Go to the newspaper of every large city in your state (many will be combined because news companies often own one newspaper in each city) and use their search tool to find craft fairs. Remember the craft fairs will start advertising for crafters about 2 months in advance.
I would advise you to ship some test items to friends to see how they hold up. You'll want to perfect that before you have to ship a real order. Look at the post office website and see if their free boxes will work for you. Also, download their software and use a debit card to print postage - you'll never have to go to the Post Office, ever. I arrange the pickups online, and then I have a white board hanging on the porch so the carrier always knows how many packages she is picking up that day. Ride herd on them the first few times, it seems they don't tell the carriers about this service, so you will be doing the training. http://usps.com
I recommend Paypal to process your credit card orders. They have a debit card you can use, so you can buy postage as soon as the customer pays you.
Have good looking boxes and packing materials even at craft shows. A good supplier for boxes and packing materials is http://uline.com
Good luck and have fun!