The confession is inadmissible, as it is protected by attorney-client privilege. Although Nirmal was in fact not an attorney at all, the conversation would have been privileged if the man Naina was talking to had actually been Badal, as she reasonably believed him to be. As a result, it is privileged.
For such an analysis, it does not matter who Nirmal actually was, who he was or wasn't affiliated with, why he deceived Naina, or whether or not he committed a crime by doing so.
There is a discussion of such situations in the following article:
Grace M. Giesel, Upjohn Warnings, The Attorney-client Privilege, And Principles Of Lawyer Ethics: Achieving Harmony, 65 U. Miami L.
Rev. 109 (2015). Available at this link
See Section IV.D.2 on page 140:
In addition to applying the honest-and-reasonable-belief analysis in
the attorney-client privilege setting to the question of representational
relationship, courts have also applied the analysis when the person consulted is not, in fact, a lawyer. The courts addressing this issue have
stated that the privilege applies to a communication even if the person
consulted is not admitted to any bar and has enjoyed no legal training. If
the putative client honestly and reasonably believes that the person consulted is a lawyer, and if the other requirements of the privilege are
satisfied, the privilege applies even though the person consulted is, in
fact, not a lawyer.
See the article for citations of cases.
Somewhat on point is US v. Tyler, 745 F. Supp. 423 (W.D. Mich. 1990). The defendant, James Tyler, shared a cell with Melvin Deutsch, who said that he was a lawyer, had a law school diploma on the wall of his cell, and was addressed as "counselor" by other inmates; but in fact was not a lawyer. Correspondence between Tyler and Deutsch regarding Tyler's legal issues was held to be privileged and inadmissible.
Tyler was held to have had a reasonable belief that Deutsch was a lawyer, in spite of the facts that Deutsch had never been licensed to practice law in any jurisdiction, and that the law school listed on his "diploma" did not exist as of the date shown on it. Tyler evidently didn't check on either of those things, and the court did not seem to think that he reasonably should have.
Also, Tyler apparently did not know the seemingly obvious fact that a convicted felon cannot practice law, let alone while actually in prison. However, this was not felt by the court to be "ingenuous": "To expect a layperson to be familiar with the internal discipline procedures of the Bar is unreasonable."
In the case from the question, it sounds like Naina was much less gullible than Tyler, and that Nirmal put on a much more elaborate and effective deception than Deutsch did. So if Tyler's belief was reasonable, surely Naina's was as well.
The article also mentions that certain states make this principle explicit by statute. For instance, the Kentucky Rules of Evidence, Rule 503(a)(3):
"Lawyer" means a person authorized, or reasonably believed by the client to be authorized to engage in the practice of law in any state or nation.
Interestingly, evidence derived from the confession is probably still admissible; for instance, if the confession revealed the location of physical evidence which the police then went and retrieved. It appears that the "fruit of the poisonous tree" doctrine generally does not apply to evidence disclosed in violation of privilege, except in some cases where the government was actively involved in the violation and thus infringed constitutional rights. See:
Robert P. Mosteller, Admissibility of fruits of breached evidentiary privileges: The importance of adversarial fairness, party culpability, and fear of immunity. 81 Washington U. Law Quarterly 961-1016 (2003). Available at this link