I made a mistake on my application too. I just called them on the phone and had to answer some questions. Then they sent me an e-mail verifying the corrections. Within 5 days I received the verification in the mail.
The thing with your appointment (if you use Pearson Vue) for testing, once you receive your ATT, there is a pretty large window of availability to choose from. I went on-line and chose the closest Pearson Vue. Then, you can also check on-line to see how many opening they have on the days you want to test. I wanted to take mine on a Friday, but it was full, so I chose Thursday instead.
Hope this helps.