1) Only take the DAT when you are READY and have STUDIED. With the exception of the ocassional troll who says they took the DAT without studying and scored a 32 out of 30, no one has ever posted that they didn't study and did well on the DAT. The DAT is the most important indicator that most dental schools use to initially measure whether you can handle a dental school academic curriculum.
2) It will take about 2 weeks for your DAT scores to reach the schools after taking the test. I took the test on July 18th and most schools had my scores by August 1st
3) It takes 6+ weeks for your AADSAS application to get to dental schools after you e-submit. E-submit the application as soon as it is ready. Take time to make sure there aren't any errors, but try to submit it early (before June 1st) and you should be fine. The 6 week mark is not always a perfectly accurate measure because it depends upon how many people submit early.
And finally, only a few schools (texas schools, Case, and maybe a couple others I can't recall) start reviewing your applications before August...so don't stress on the timetable too much unless you are e-submitting late in July or Takeing the DAT in late august. Timing is important, and early is best, but it is okay to submit a little later...it will just lower your chance of acceptance and delay how early you hear back...but it doesn't completely kill an application.