You should apply before arraignment. You cannot apply at court.
The judge will impose a bond for DUI 1st at your arraignment. A lawyer with experience with that judge can advise how much bond to expect. It should not be high given your lack of criminal history.
Unfortunately Miranda warnings will have no bearing on your DUI case. This is a common misconception and your lawyer can explain why.
Polygraphs ARE admissible in New Mexico and Massachusetts. Your public defender is right. If you pass, he provides a copy to prosecutor and pushes for a dismissal. If you flunk, he tosses the results in the trash. Either you are not being honest with your lawyer or you are not trusting him. To be effective your lawyer needs both.
If he does time just for DUI probation violation, the DUI conviction will not prevent renewal of his resident alien card. If they convict him of possession of cocaine he would not only be deported but he would never get his papers back. He may want to turn himself in for the DUI and see what happens. He has little to lose that he hasn't already thrown away
Check with an ImMigration lawyer too on how to proceed.