In addition to what the above poster said, you register for the DAT through prometric, you can check the dates of availability, and where its available by going to their website. For me, there was like 4 within 20-30 minutes driving, each with different available days/times. The earlier u register, the better chance u get of getting the day you want.
With regards to the second question, it is definitely different for everyone. I've been pushing back my DAT for forever because I dont feel ready haha, so its really whenever you think you are prepared.