Is there any way to bring a criminal case before the grand jury without the support of the Prosecuting Attorney? Is there any way to present a case to the grand jury if the prosecuting attorney is unwilling to do so?
To answer the first question, the answer seems to be "generally not." In federal courts, this is explicitly not allowed -- rule 6(d) of the Federal Rules of Criminal Procedure states that the only people who can be present before a grand jury are government lawyers, the witness being questioned, interpreters, and a court reporter In state courts, the rules vary by state. However, again, private citizens are generally either completely not allowed to act as prosecutors, or are only allowed to act as prosecutors in a restricted set of situations and subject to the ultimate control of public prosecutors. For instance, in Virginia (which allows private prosecutors), the private prosecutor can't speak in front of a grand jury, initiate a criminal case, or participate in a decision to dismiss charges (page 23). In New Hampshire, private prosecution is limited to misdemeanors with no possibility of jail time, and again the state can dismiss charges (page 8). Rhode Island, like New Hampshire, allows private prosecution for misdemeanors but lets the state dismiss charges (page 11). The justification for allowing the state to dismiss charges is generally "prosecution is inherently a governmental task, so the government must retain ultimate control."
The plea is entered before the trial. The concession of guilt happens during trial: the lawyer acknowledges that the defendant did the crime, but argues that it should be overlooked in some way. For example, Nixon dealt with a death-penalty case where the lawyer's strategy was to admit during the trial that the defendant had killed the victim, but to use the trial to persuade them that the circumstances did not call for the death penalty. You don't get to make those arguments if you enter a guilty plea, which would then strip you of your right to a jury.
The constitutional provision quoted in the question has been interpreted to require that a jury trial be available to a person accused of crime by the US Federal Government. Then accused is free to waive this right, and be tried by a judge only if s/he so chooses. The accuse is also free to waive the right to a trial altogether, and plead guilty (or &quot;no contest&quot; which waives a trail without an admission of guilt). The provision could reasonably be interpreted to require that if there is a trial, it be by jury. But I don't see how it could reasonably be read to require trials in all cases, and forbid guilty pleas.
The rules of criminal procedure are going to differ from jurisdiction to jurisdiction. In US federal court, for example, a criminal trial in absentia can happen, but only in limited circumstances. See Fed. R. Crim. P. 43. A notable example of a defendant not appearing for a federal criminal case is the recent case, arising from the Mueller probe, against Concord Management and Consulting LLC (a Russian entity).
So I'm fascinated with the OJ trial and I've read a ton about it. I'll try to answer your question both accepting your premise as true, and then also going into what actually happened. First of all, jury nullification cannot be overturned in the US. The double jeopardy clause forbids it. This is such a powerful tool, in fact, that there are strict rules that prevent defense lawyers from mentioning or even hinting at jury nullification, in front of the jury, in almost all circumstances. It doesn't mean D is safe from all legal liability. OJ, obviously, was found liable in the civil trial. Sometimes other jurisdictions can prosecute. For example, after the officers in the Rodney King beating were acquitted in state court, the federal government got them for violating federal hate crime statutes. Second, looking at your premise. If jurors think D is guilty, but also being framed, that's not necessarily jury nullification. Remember, a criminal defendant must be proved guilty beyond a reasonable doubt. That means that 'probably guilty' means 'not guilty.' That said, there may be times when a jury is convinced beyond a reasonable doubt of a defendant's guilt, but is so disgusted by the police tactics used in the case that they acquit. This would be jury nullification. What actually happened in the OJ case: Mark Fuhrman perjured himself on the stand. He lied and said he'd never said the N word, and the defense produced tapes of him saying it a ton. The defense recalled him to the stand. Because perjury is a serious crime, this time he came in with his own defense lawyer, and did nothing but take the fifth on the stand. In a genius move, OJ's defense team asked him whether he planted any evidence in the OJ case. He didn't deny it, instead he took the fifth (again, as he was doing to every question). This was enough to sow reasonable doubt about OJ's guilt based on the evidence in that trial (there's obviously no actual doubt, in real life, that he's guilty). So, what actually happened wasn't jury nullification.
You could bring a motion to compel for failing to respond substantively to a motion to admit which is objected to, just as you could for an interrogatory. The process is the same. Normally, a request to admit would not be deemed admitted if a substantive objection was filed by the deadline, even if there was no express admission or denial. Only if the objection were completely and utterly meritless would a judge be likely to order that the request to admit would be deemed admitted in that case since the response was a de facto non-answer and the objection was a mere sham. @Iñaki Viggers states in his answer: the purpose of a request for admissions is [to attempt] to stipulate --rather than to discover-- the facts on which plaintiff and defendant agree. This is not really true. A request to admit is a discovery tool to prevent you from having to prove up what should be non-controversial facts that might nonetheless take time or documentation to prove at trial and to gather evidence for in advance of trial. The questions in a request to admit are typically ones that the other side would not willingly stipulate to (for example, because they'd like to be able to offer testimony to explain a seemingly unfavorable fact) but may not be able to deny. If a party denies a request to admit and then offers nothing to support the denial in discovery practice or at trial, that party risks court sanctions for the groundless denial. Good litigation practice is also always to include some requests to admit that are effectively outcome determinative to give the opposing party a chance to screw up and essentially default the case by not responding on time.
It happens all of the time, even though it is mildly improper. Usually, the lawyer can get away with it until the judge sternly warns the lawyer not to try it again, in which case the lawyer risks being held in contempt of court. This is riskier for a prosecutor (who risks this conduct causing a conviction to be overturned on appeal resulting in a new trial), than for a criminal defense attorney. This is because an acquittal, if obtained by these methods, is still not subject to appeal. Indeed, for a criminal defense attorney, even if it results in a mistrial followed by a new trial (which can be allowed if the mistrial is caused by the conduct of the defense), the mistrial will often count as a win if the trial was going badly on the merits.
No, there is no recourse. An yes, the potential "costs", both personal, financial, social, can be high and are not compensable under an investigatory hold scenario; however, it doesn't usually happen like that. There is no investigatory hold that long without arrest. If the police want to talk to you but don't have enough to arrest you, you can leave any time. If you call your lawyer, he/she will come to the police station and tell the cops to release or arrest you. If the police really want you to stay, likely there is probable cause and they can keep you anyway. The police can arrest you and keep you, without a warrant so long as there is "probable cause" to believe that a crime has been committed (by you). Once arrested without a warrant, this is what is usually referred to as an investigatory hold, where the law says you must be arraigned within 72 hours (some states it must be 48 hours, 1 day less than supreme court says is reasonable). During this time they can investigate their case against you and decide what, if any, charges they will bring. There is no recourse for this, (in the event they bring no charges) unless you can establish that you were held for no reason (including not being falsely identified) and that it was only to intentionally deprive you of your right to liberty. This is nearly impossible to prove, unless you really did nothing and the cop was just messing with you (for instance in a personal vendetta) and you can show that.