Are there any legal requirements or regulations for a private university to prohibit sexual relationships between faculty and students? Hypothetically speaking, could a private university in the USA not prohibit consensual sexual relations between students and faculty because their policy did not include it or the wording in said policy was poor or unclear? My novice understanding is that private universities have more leeway when it comes to their rules and several ethical subjects seem to be enforced through 'contract law' based on their own policies.
The only time that this conduct has to be prohibited in a private university is when state or federal law prohibits it in any case. In those circumstances, no separate university policy to restate the applicable law is required. Best practices are to make students and teachers aware of any applicable laws, because knowing that, the the parties are less likely to be involved in illegal conduct. But private universities aren't required to adopt policies of that type if they aren't bothered to do so. With federal grant funding, private universities are required to have a mechanism in place for addressing sex discrimination complaints, but the policy doesn't have to articulate that particular conduct is or is not prohibited, beyond what federal law provides in the absence of a formally adopted policy. Incidentally, a few private colleges, almost all religious, specifically decline federal funding in order to be free of the regulations and strings that come with accepting it. Also, while private universities are not required to have such policies legally, private universities are required, as a matter of practical reality (e.g. in order to be considered eligible to borrow money from banks and to be eligible for many charitable grants) to have liability insurance in place, and liability insurers will often insist that their insured have certain policies in place, especially if the insured private university has a history of prior claims of this type.
In the US, only a few states allow conjugal visits by prisoners: California, Connecticut, New York and Washington. Details of implementation for Washington are here (it is called "Extended Family Visiting"). There are various limitations, for example you can't have committed homocide within the last 5 years, you can't be on death row, and so on. Although they don't explicitly say you can have sex, you can, and they have (a small sample of) contraceptive and STD-preventing technology for prisoners to avail themselves of. If you fail to take advantage of contraceptives, then yes it is possible. There is no provision pertaining specifically to mass murder.
The tort for this kind of activity is called public disclosure of private facts, and almost every U.S. state recognizes that this tort is invalid under the First Amendment in the absence of a legal duty not to disclose of the type existing between an attorney and client, or a psychotherapist and a patient, or a contractual non-disclosure agreement, that does not exist between roommates. There is nothing illegal about your roommate's conduct. Your best move at this point is to take responsibility for your own conduct, to repent and to convince the world that you're doing your best to get on the straight and narrow going forward. If your former roommate insisted on payment for not disclosing the information, that would be extortion, but there is nothing wrong with going ahead and disseminating it without trying to obtain something of value from you for not doing so.
In some jurisdictions it's against the code of ethics. For example, in the united-states, Model Rule of Professional Conduct 5.4(b) says: A lawyer shall not form a partnership with a nonlawyer if any of the activities of the partnership consist of the practice of law. The idea has to do with independence: Lawyers are officers of the court and—as members of a regulated profession—can be bound to professional codes. Talented leader/organizer/visionaries aren't bound in any such way. The comment to the Rule explains, "Where someone other than the client pays the lawyer's fee or salary, or recommends employment of the lawyer, that arrangement does not modify the lawyer's obligation to the client." This can create a conflict, and states resolve it by regulating the partnership's composition. Other jurisdictions go even further and it’s prohibited in law.
You may be mistaken about the purpose of the Miller test. If some content is obscene according to the Miller test, then it does not receive First Amendment protection, and could be prohibited from distribution by the government. However, it says nothing about the contractual obligations that two parties can agree to. To the extent that the obligations themselves are objectionable this analysis would fall under the doctrines of unconscionability and public policy.
Context is important. There is no law against taking a picture of a child who is entirely naked or exposing certain body parts. The laws in question such as 18 USC 2251 refer to the fact that the minor "engage[s] in, any sexually explicit conduct". Sexually explicit conduct is defined in 18 USC 2256, and would include "lascivious exhibition of the genitals or pubic area" (which does not include nipples of anyone). Federal law does not define "lascivious", but the ordinary meaning of the word does not include the situation that you describe. The Justice Department, which goes after child pornographers, provides this guide to federal child porn laws. Georgia's child porn law is only marginally different, referring to "Lewd exhibition" rather than "Lascivious exhibition" , and including the "Condition of being fettered, bound, or otherwise physically restrained on the part of a person who is nude" (so a picture of a person holding a naked baby would technically qualify, but is highly unlikely to be prosecuted as production of child porn). These laws pertain to any form of child porn, including "private use only". Dissemination would be an added charge.
Setting aside everything but the title, the Title IX coordinator does not have a federal obligation to email questions to anyone. They may, however, have an institutional obligation to act in a particular way, which might include always email questions, or never emailing questions (the latter is most likely). Assuming someone filed an institutional grievance against you, you have some right to answer these charges – it will be spelled out in the institution's rules. The federal regulations are between the institution and the government, and the institution then creates rules to keep themselves in compliance. The usual worst-case scenario is that someone files a grievance, which is reviewed by the institution. As the accused, you will be informed of the charges against you, and will have the opportunity to defend yourself at least by the "committee decision" phase. Prior to that point, the institution can gather any data deemed relevant, and may well require that all questioning be conducted in a face-to-face meeting. Universities generally have minimal specification of procedural requirements, until they run into a problem and impose rules. To determine a person's authority to require something of you, you can ask them to tell you the university rules that give them that authority. Your attorney can then compare their demand with their authority and advise you whether you must comply, or perhaps strategically should comply, or should refuse. The federal regulation which drives this is 34 CFR 105 subpart A. The logic of this is that the institution cannot discriminate on the basis of sex, if they do, they can be punished, but they can also "erase" the discrimination if they "overcome the effects" of the discrimination. §106.8 requires the institution to have a coordinator who assures compliance and does what is necessary including investigating. There must also be a grievance procedure: (b) A recipient shall adopt and publish grievance procedures providing for prompt and equitable resolution of student and employee complaints alleging any action which would be prohibited by this part. There is absolutely no further federal specification as to what this coordinator can do, instead the government leaves it up the the institution to come up with procedures. The only requirement is that there be no judgment of discrimination.
You cannot contract outside the law Any "contract" that purports to break the law isn't a contract - it's an unenforceable agreement. For example, across all jurisdictions, a contract that is unconscionable is void. So is a contract that requires one of the parties to break the law - a "contract" for murder for example. In addition, you cannot call an employment relationship a "business" relationship - if the relationship meets the requirements of an employer-employee relationship then that's what it is and woe betide you if you haven't complied with all relevant entitlement, tax, insurance and safety laws. In addition, all of the relationships you listed are contracts.