Are defendants legally obliged to provide all culpatory evidence to
prosecution?
The question here is whether or not all evidence requested by
prosecution must be provided by the defense? If the defense plans on
only using the evidence of the prosecution, does the prosecution get
to demand evidence the defense would rather not release?
No.
Usually only specific kinds of evidence related to specific kinds of claims such as alibi evidence, an insanity claim, or expert testimony must be disclosed prior to trial by a defendant in a criminal case.
A defendant in a criminal case does not have to disclose evidence harmful to the defendant's case prior to trial as a general rule.
Sometimes there is a requirement to disclose witnesses anticipated to be called, or exhibits to be possibly used very shortly prior to trial, but that is more the exception than the rule.
Does the answer depend on the whether or not the case is criminal or
civil?
Yes. A plaintiff in a civil case can compel disclosure prior to trial of all evidence in the custody, control, or possession of the defendant that is relevant or is reasonably calculated to be relevant to a disputed issue identified in the complaint, answer, and other pleadings (e.g. counterclaims, replies to counterclaims, third-party complaints, cross-claims, etc.). The scope of discovery is slightly different in jurisdictions that don't follow the federal model.
This can include pre-trial depositions of the parties, although a defendant can claim the 5th Amendment at the risk of being exposed to an adverse inference communicated to the jury at trial if the defendant does so.
Furthermore, most jurisdictions require the pre-trial disclosure of expert testimony that will be used at trial, of exhibits that will or may be used at trial, of witnesses who will or may be called a trial, of all documents that are relevant to a disputed issue identified in the complaint, answer, and other pleadings, of all insurance coverage that could cover the claim, of all persons with knowledge of the disputed facts, and of an expected damages calculation. In the federal system, however, one need pro-actively disclose only witnesses and documents that support your case without being asked.
Is there consistency on this or is it at the discretion of the judge?
The rules of procedure applicable to a case govern the scope of discovery, but judges have considerable discretion to determine that requests are excessive relative to what is at stake in the case, are irrelevant, or unduly burden some other legitimate interest of the person subject to discovery.
Is there punishment for non-compliance?
Yes. First of all, a failure to disclose when there is a duty to do so is a ground to exclude presentation of that evidence at trial. Secondly, in civil cases, attorney fees incurred to obtain the discovery can be awarded, facts that might have been disclosed can be declared to be true as a matter of judicial sanction where there is not disclosure, claims can be dismissed, etc. The main relevant federal rule in civil cases is Federal Rule of Civil Procedure 37.
It is an unlawful request that must nonetheless be followed with only
a hypothetical remedy left to the defendant as is the case in most of
these united states to comply with an obviously unlawful arrest that
doesn't present an immediate threat to life?
I don't understand this long and convoluted sentence. The part about an unlawful arrest seems divorced from the issues in the rest of the the question. It isn't clear what kind of unlawful request is involved either.