1. It's up to you. I brought my car and was very happy I did. It was a 9 hour drive to Cincinnati for me. Hotel will provide transportation to training center and limited transportation in the area. Also, other classmates will probably have cars so it's not that big of a deal if you don't have your own transportation. Remember, training is 2 months..just depends on if you think you can be without your motorcycle for that long.
2. After training, it all depends on how backed up they are with IOE. I waited about 2 weeks to start IOE, plenty of time to move. After IOE, you'll be put on reserve pretty much the next day so you'll want to make sure you're moved in by then.
3. Business casual.