It should be granted. If it is not granted within a reasonable time, you may want to hire an immigration attorney to assist you.
Mr. Shusterman's (former INS Trial Attorney, 1976-82) response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
Sorry, but it doesn't look good. Your application will likely be denied and you'll receive the denial notice in the mail soon.
Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
Generally speaking, "post decision activity" would be indicative that a denial notice is being prepared. However, without knowing the specifics of your criminal history it is impossible to predict with any certainty. You use of the term "no prosecution" can have multiple meanings (as crazy as it may sound) in the immigration context. Consult with an experienced immigration attorney who can review your criminal records and advise you what to expect.
While this answer is provided by a Florida Bar Certified Expert in Immigration and Nationality Law, it is for general information purposes only and an attorney/client relationship is neither intended nor created. You should seek out qualified counsel to review your case and provide you with advice specific to your situation. Review Mr. Devore's Avvo Profile for more information about his expertise in immigration law and how to contact him to discuss your case.
If your disposition was actually nolle prosse and you do not fall within any other category for denial, it should be granted. However, we cannot speculate about your decision without having the benefit of reviewing your case. If you are concerned, it's time to meet privately with an attorney.
Answers provided by Ksenia Maiorova, Esq. on Avvo.com are of a general nature and do not constitute legal advice.