No. The granting of Deferred Adjudication is not strictly limited to a specific docket setting on a case.
However, there is no guarantee that any particular case will be entitled to that resolution. Some prosecution offices have policies to when they make the 'best offer available' and that can affect the timing your decision to plead.
The best advice is to retain a lawyer that regularly works in the courts where you are charged. That attorney will know the regular practices of the court and the prosecution and will be situated best to advise you on your options.
Not at all. In fact, if you want to get deferred prosecution, you and your lawyer will have to put together a packet of information to try to convince the prosecutors that you should received the special agreement.
If you receive a deferred adjudication offer, you will have time to consider whether you want to accept the offer.
Listen to your lawyer's advice and help the lawyer as s/he requests.
In a criminal case, there is what I like to call a plea negotiation phase. The district attorney will look at many different factors to determine if he wants to offer deferred adjudication. Usually the district attorney will allow you time to think about an offer. A criminal defense attorney should be able to help you through this process and help to persuade the district attorney to look at factors favorable to you.