Floors, Lilo gave you excellent answers to your questions. I'd like to add to what he said:
1) I'm not sure there is a normal percentage for plea bargaining. It varies by prosecutor, state vs. federal cases, the severity of the crimes, the amount of public attention, whether or not the prosecutor is up for election, and especially what previous criminals got.
Judges and prosecutors hate trials because they are costly and time consuming. That's why most criminal cases result in guilty pleas after plea bargains. But, as Lilo pointed out, the "political" factor is very important. Plea bargains are most likely to be offered when the crime is "victimless" (i.e., gambling or assault on another criminal). But you'll seldom see a plea bargain in a case of child molestation--everyone hates a child molester, and a prosecutor will get no thanks from the public for going easy on that kind of felon.
2) No. No population register here. There is SS of course and a few other ways to get just about everyone's identity but I think the main reason witness protection works is that the US is a huge place with a relatively mobile population.
America is almost schizophrenic about "privacy." On the one hand, we've passed many laws in the last 20 years safeguarding privacy of Social Security numbers, records, etc. On the other hand, with electronic record-keeping and the Internet, it's easier than ever to find and "steal" another person's identity. Witness Protection Program identities and addresses are supposed to be ultra-secret. But records are kept, and if enough money is spread around...
3) Yes, in plea bargaining the prosecutor can agree to drop certain charges. Something that many prosecutors do is to overcharge in order to have some leverage to convince a defendant to take a deal.
That's especially true here in Arizona. This is a major venue for methamphetamine production. Police are always capturing moron criminals who commit stupid traffic offenses (like speeding 25 mph over the limit) while carrying large quantities of drugs, plus drug paraphernalia like pipes, bongs, scales, etc. So the police will not only charge them with a felony (possession of illegal substance with intent to sell), but also with possession of drug paraphernalia (another felony). If the criminal talked back to police, they'll charge him with resisting arrest--another felony. And the speeding? They'll charge him with "attempting to evade lawful arrest" (another felony). By the time all those felony charges add up, the guy's looking at about 100 years in prison. So, prosecutors offer him a deal: Plead guilty to possession of drugs with intent to sell, take a 7-year sentence, and they drop the other charges.
4) Ultimately it's up to the prosecutor to decide if he (she) has enough to bring a case. They may not want to bring a case at a given point in time because the facts are weak or they aren't ready to disclose investigative methods, undercover agents or informants or any number of other reasons. In a lot of cases, though particularly organized crime ones, there are multiple jurisdictions, so where one prosecutor/law enforcement group may demur bringing charges, another one may charge ahead. This happened in NY with Gotti when US attorney went ahead with a case, despite conflicts with the FBI, and revealed to the FBI's displeasure that Gotti associate Willie Boy Johnson was an informant.
"Multiple jurisdictions" is important. Here in America we have local courts that hear misdemeanors (offenses like shoplifting, simple assault, theft of less than $1000) that carry maximum sentences of less than one year in prison. County and state courts hear felony cases--anything up to and including murder--that carry sentences of more than a year up to and including the death penalty.
Federal courts hear cases that violate Federal laws or that have an "interstate" component. An obvious Federal offense: counterfeiting (only the Federal government prints currency), or treason (only the Federal government can prosecute spies or traitors). But lots of local and state crimes can have an "interstate" component. For example, if you steal a car in New York and cross over into New Jersey, you could be prosecuted in a Federal court for "interstate transport of stolen goods." How are such cases decided? Sometimes the requirements of proof in one jurisdiction make it easier to prosecute there than in another jurisdiction. For example, in order for Gotti to be convicted in a New York State court, the prosecution would have to prove that he committed an actual crime, and produce two witnesses to testify to his crime. But in a Federal court, he could be tried under the RICO Act, which only requires the prosecution to prove "conspiracy" to be part of a criminal organization, and doesn't require a corroborating witness.