To begin with, jury nullification is not a separate act. It’s not like the jury verdict can be one of “Guilty”, “Not guilty” or “Nullified”.
Instead, a juror says something like “The guy’s pretty sus for sure, but I’m voting not guilty because [insert reason that’s contrary to applicable law]”. Others agree and find the defendant not guilty. To anyone who has not taken part in the deliberation, the outcome is indistinguishable from what would happen if the jury found a glaring hole in the evidence.
Any judicial system where 1) juries exist 2) they vote for whatever they want and 3) they can’t be prosecuted for how they voted will automatically have jury nullification.
[J]urors... go to the judge himself to ask about jury nullification
Exactly this happened in United States v. Sepulveda.
Can the judge flat out tell the jury that they cannot vote to nullify the verdict?
That judge replied:
Federal trial judges are forbidden to instruct on jury nullification, because they are required to instruct only on the law which applies to a case. As I have indicated to you, the burden in each instance which is here placed upon the Government is to prove each element of the offenses . . . beyond a reasonable doubt, and in the event the Government fails to sustain its burden of proof beyond a reasonable doubt as to any essential element of any offense charged against each defendant, it has then failed in its burden of proof as to such defendant and that defendant is to be acquitted. In short, if the Government proves its case against any defendant, you should convict that defendant. If it fails to prove its case against any defendant you must acquit that defendant.
He didn’t really say anything new here, other than declining to answer the question directly and reiterating jury instructions, the official template of which includes the following:
If, after fair and impartial consideration of all the evidence, you have a reasonable doubt as to [defendant]’s guilt of a particular crime, it is your duty to acquit [him/her] of that crime. On the other hand, if, after fair and impartial consideration of all the evidence, you are satisfied beyond a reasonable doubt of [defendant]’s guilt of a particular crime, you should vote to convict [him/her].
Logically speaking, this expressly forbids jury nullification, as it demands that the jury acquit the defendant if and only if they have the reasonable doubt, and nullification is the opposite of that. However, this prohibition is without teeth as there are no consequences for violating it. It isn’t even worded in terms stronger than “duty” and “should”.
If the judge did so and the jury chooses to nullify the verdict anyways would the fact that the judge forbade them to do so have any impact on what happens from that point forward? Would the jury risk repercussions for nullifying a verdict against the judges orders?
A juror can be held in contempt of court for certain actions such as researching something on their own, but they can’t be prosecuted for how they voted.
Finally is there any situation where jury trying to nullify a verdict could phrase their objection incorrectly such that the judge could rule it as a guilty verdict (ie if they say "we think you proved the plaintiff did this thing, but we don't believe he should be punished" can the judge rule that they said he was guilty and just ignore the second half?)
Each juror votes guilty or not guilty. The overall verdict then is either unanimously guilty, unanimously not guilty, or not unanimous (hung jury). Neither the judge nor anyone else is at liberty to switch it from one of those three to something else—regardless of whether the jury for some reason chose to explain their verdict, which they aren’t supposed to do.
To summarize: the judge can flat out tell the jury that they cannot vote to nullify the verdict. The jury is free to disregard this with no repercussions. What will happen on appeal and whether there will be grounds for mistrial is a different question.