He may be eligible for cancellation of removal but it will depend on the first offender statute and how immigration treats that particular law. In some states this type of offense with a first offender result is a conviction for immigration purposes but in some states it is not. The possession of ecstasy offense is not a problem because it was dismissed. The DUI is not a deportable offense so is not a problem. There are other requirements for cancellation, 10'years in US before commission of a criminal offense or placement into removal proceedings, good moral character, a qualifying relative ... He needs a lawyer.
The answer provided here is general in nature and does not take into account other factors that may need to be reviewed for a more precise answer. You should consult with an immigration attorney before taking any action. The answer here is not intended to create an attorney-client relationship.
Agree with Mr. Murphy, but would like to add that I think the ecstasy charge could create an issue with "reason to believe" he is a drug trafficker depending on the circumstances and the amount (Mr. Murphy is most likely correct, but I prefer being paranoid and extremely cautious). He definitely needs an attorney and then he should know what options may be available to him and the risks associated. If you want to help him, consult with an immigration attorney or two with experience in detained immigration cases (really he should, but may not be able to very easily as he is detained) and help him select one he is comfortable with.
All of the previous answers are very good. What you need right away is a consultation with an immigration attorney who can begin to work your case immediately. Every case is different and although many facts seem similar it is important to have the case evaluated for probable remedies. If you would like a consultation please feel free to call us at: 770-559-4935.