I'm Lucy, and I'd be happy to answer your questions today.
The first part of your question I answered on another page.
It is the judge who conducts pre-trial hearings. Either the prosecutor or the defendant may request one. The prosecutor can INFORM the defendant that he will object to evidence being admitted but (a) the defendant can offer the evidence anyway and (b) the prosecutor cannot give a defendant legal advice.
The prosecutor MAY re-represent the initial settlement offer after trial, but it's extremely rare. If the defendant wins, he's not going to accept a deal, so there's no point in offering, because the prosecutor can't appeal. If the state wins, they nearly always ask the judge for a harsher penalty than what was in the original offer. The defendant typically does not get to pick his sentence if he's lost at trial, but there is frequently a pre-sentence report, which is written by the DA and submitted to the court, with a copy to the judge. The judge doesn't always order a sentencing report for minor misdemeanors, and the DA can make their recommendation orally to the judge in open court. In that scenario, the defendant wouldn't get anything in writing.
The court doesn't make offers, so I'm afraid I don't understand your last question. The court simply issues a sentence. He can repeat what the DA is offering, but he's not making that offer. But the judge CAN tell the defendant if it's in his best interests to accept and offer from the DA - in that case, he's actually doing the defendant a favor by not just imposing a harsher sentence than whatever is being discussed.
If you have any questions or concerns about my response, please reply WITHOUT RATING. It's important that you are 100% satisfied with my courtesy and professionalism. Otherwise, please rate my service positively so I am paid for the time I spend answering questions. If you are on a mobile device, you may need to scroll to the right. There is no charge for follow-up questions. Thank you.