There is always time for the prosecutor to drop the case. Often, the case will be dropped just before the jury is sworn in.
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If you are asking whether it is possible for the state to drop charges before trial, the answer is yes. If you are asking whether the state will drop the charges before trial, the answer is not predictable. The decision whether or not to go forward with criminal charges is up to the prosecutor and the fact they have decided to offer a plea is not necessarily an indication that they can't prove the case. Prosecutors have heavy case loads and need to resolve some cases. They cannot possibly try them all. While an offer to drop charges in exchange for a plea agreement can mean the state will have proof problems at trial or that the state will drop the charge is you push them, it doesn't have to mean that.
Regarding the possibility of challenging the charges prior to trial, then answer to your question is yes. There are ways to challenge charges prior to trial. One such way is through a motion to dismiss. Typically, a motion to dismiss admits the facts the state has alleged and then argues that the facts as alleged do not constitute a crime. A motion to dismiss admits that you are not disputing any of the facts alleged by the prosecution. If that is not the case, your attorney probably will not file a motion to dismiss.
There may be other ways to challenge the evidence the state has against you prior to trial. Ultimately though, you will have to make a decision about whether you are willing to risk the possibility that the state is willing and able to prove its charges against you. To help you make this decision, you should have an experienced criminal defense attorney that you trust.
As a practical matter, none. You are only getting the more serious charge dismissed in exchange for pleading guilty to the reduced charge. You will be convicted at that point. If you withdraw your plea you will go to trial on the original charges. Generally questions of whether the evidence proves guilt or not is for a jury to decide. Don't expect much sympathy with this type if charge.