Got arrested by ICE beginning of November. ICE gave me the first master hearing towards the end of January. Went to court, Judge explained the procedures of the court, our options. We wanted to apply for asylum. Judge asked how much time we would need to submit the application and evidence. We wanted one month's time. Our lenient Judge gave us two month. In his words, he did not want us to feel rushed. Showed up two months later for the second master hearing with our application and evidence. Then we had to wait 5 months for the individual hearing and then two months later we had the decision hearing.
As far as EAD is concerned, you clock has to have run for over 150 days. Your clock starts when your case starts. It is stopped anytime you request extra time.
Hope this helps.