I think the question is essentially, 'how does the law work in practice?'
Now, my questions are very broad so please do not focus on the
specifics of this example.
The law is a huge bag of specifics.
(1) How exactly does the "rubber meet the road" when it comes to
statutes, and laws more generally?
If someone sends you a letter saying 'you broke the law', who cares? Depending on who is saying it, maybe you care. If your bank account stops working, or if the police haul you off to jail, then you definitely care.
It doesn't mean anything to merely say that something is illegal or obligatory. The law must provide for specific means of enforcement. Many prohibitions are backed by the criminal justice system, which is to say that breaching that law is 'an offence' and you may go to prison for the length of term specified in the law.
A law will often provide for a government agency to enforce it. For example, in Australia, the law says you must pay the minimum wage, and the law also creates an organisation called the 'Fair Work Ombudsman' which (again, as prescribed by law) can issue fines to employers who underpay workers.
As per Dale M's answer, the default enforcement mechanism is 'the court'. (You need to read a book like Baker's 'An Introduction to English Legal History' to understand exactly what a court is and why it has the specific powers it has.) But there still has to be a law that says something like 'the Supreme Court may make orders to enforce this statute' or 'a person who X may sue in the Y court for compensation from a person who Z'. For example, section 11 of the Freedom of Information Act (Cth) in Australia says 'every person has a legally enforceable right to obtain access [to government documents]' but you cannot go to a court to get an order to enforce this right. Enforcement, as prescribed in that Act, is via the Freedom of Information Commissioner and the Administrative Appeals Tribunal.
For an interesting story about enforcement, look up the Defence of Marriage Act ('DOMA') in the United States. DOMA was enacted and then, after an election and a change of President, the new President decided he didn't like DOMA. But he didn't have the numbers in Congress to actually repeal it. So he just stopped enforcing it. Specifically, he lost a court case (Windsor v US) where the judge thought DOMA was unconstitutional and he didn't appeal it. Ordinarily, if a trial judge declares your statute unconstitutional then you appeal all the way to the Supreme Court to get your statute enforced, and meanwhile keep telling everyone that your statute is valid. Windsor v US left the law in a funny state: same-sex married couples had to decide whether they were allowed to claim tax concessions as spouses but, since the interpretation of a trial judge could be overruled by an appeal court in a later case, they had no real certainty. The taxpayer who won the court case at trial couldn't appeal to a higher court, because she won. The Government lost but it didn't want to appeal. The courts ended up doing some weird stuff procedurally, allowing representatives of part of the legislature to join suit to attempt to enforce DOMA, which drove the case up the court hierarchy to the Supreme Court, which agreed with the lower courts that it was unconstitutional: US v Windsor (2013) 570 U.S. 744. The point of including this story is that the law is not just about statutes and formality, it is about flesh and blood people on the ground and their desire to do or not do something.
It would make sense that a large townhall-esque meeting should be
open, but is a meeting between two lower-level employees covered under
the law? Sure, it can get definitional, but the broader question would
be how are those definitions determined.
The simple answer is that courts decide what statutes mean. This is almost always correct but the reason is not that simple.
Whoever is enforcing the law will form a view of what they think the law means in the circumstances at hand. In Australia, for example, the Australian Taxation Office decides what it thinks the tax law means, the police decide what the Crimes Act means, managers in the public service decide what the Australian Public Service Code of Conduct means, etc.
If a dispute ensues, it will often end up in court. In Australia, every dispute involving a government official can end up in court because our courts have a generous view of what are known as the 'perogative writs', namely certiorari, prohibition and mandamus or, in English, 'give me the case file', 'stop doing that' and 'do your job properly'. This is called 'administrative law', it comes up a lot in Australia with respect to asylum seekers, and it boils down to: if an official claims to be acting under a law, and they misinterpret that law (which is to say, the court has a different view of the relevant law) then the official could not be said to have been acting under that law and so the court will declare that official's action invalid.
Who can issue which perogative writs to which government officials in respect to which laws? Generally: 'the courts'. Specifically: depends on the statute at hand. Sometimes a constitution or two are involved.
So, like I said, the courts would decide whether a particular circumstance meets a particular definition.
(2) How could Billy determine the nuances of how the statute is
enforced? A plain reading of the state statute is easily accessible
online and clearly states that Billy is allowed to attend public
meetings. How could Billy research how the statute is currently
interpreted by the powers that be and know exactly what it means in
practice?
If there is an enforcement agency involved, they may have information. For example, if you want to know how Australian securities law works then you can look at the website of the Australian Securities and Investments Commission. Interestingly, this does not work with the police: I have not seen a police force's website with information about the criminal law on it. In recent years in Australia, groups of judges have started to publish 'bench books' which summarise the law on particular topics, which has the side effect of letting lawyers and members of the public see how those judges (probably) intend to administer those laws.
Most of the time, laws are obeyed without fuss (to be specific, the authorities' view of the law is obeyed without fuss; the authorities may of course be mistaken about what the law is) and the most disputes are resolved without going to court. There may be a whole body of practice (not really 'law' as such) which is only known to the relevant government agency and the lawyers who regularly represent people interacting with that agency.
If a dispute gets to court and the court rules on the meaning of a law, it may appear in what is called a 'law report'. The US Supreme Court is an important court, so basically everything they say is reported, but for lesser courts not everything is reported as widely. Part of the idea of law reports is that you can look up the cases on the issue you're interested in and see how the courts are ruling. This assists you to predict what they will do in your case, which is of course impossible but you can at least assess your chances of success.
There are also books. Before I studied law, it never occurred to me that if I went to the public library there would be a book called 'Contract Law' which would explain contract law to me. It's not easy to read but it's there.
(3) Assuming some "workable arrangement" or "agreed interpretation" of
the open meetings statute is in place (for example, let's say meetings
are public if and only if they have more than three officially
scheduled attendees including the organizer), under what circumstances
and how could this be changed? Let's say Billy wants to re-define
meetings as any scheduled conversation between two or people. Can
Billy do this?
This is an example of administrative practice, which is like case law but consists of decisions by officials other than judges. Billy might just have to be very persuasive (i.e. get the officials to change their practice), or maybe Billy needs to take someone to court. Sometimes administrative practice hums along for decades, until someone asks the right question in court (or the wrong question, depending on how you look at it) and the long-standing practice is revealed to have been illegal. For example, for decades in Australia we had a quasi-court setting wages and working conditions and also enforcing those conditions; it turns out that was prohibited by the Constitution. Whoops!
Sometimes the administrative practice is not just administrative practice. Sometimes the law allows a particular authority to issue regulations or rules which govern procedure or fill in gaps in the legislation. In this case Billy would have to wait until the next review of the regulations (e.g. sometimes regulations 'sunset' after five years) and make a submission at that time.
(4) What if Billy is completely in the right and is technically
allowed at any meeting he wishes to attend, but university officials
have no respect for the law. They kick him out every time. What
recourse does Billy have? Could Billy call police on security when
they try to kick him out? What if the police are friendly with the
security guys and laugh at Billy like everyone else? Who does Billy
call then?
I believe in objective subjective objectivism. That is, there is such a thing as the absolute truth on all questions and those truths are knowable, but everybody else is wrong about them and that's the truth. So what does it mean for Billy to be 'right'?
Metaphysics aside, legally, maybe Billy can go to a court. Outside of the law, maybe the media, or perhaps persuade donors to apply pressure on the university officials. How did Frank Underwood become President?
(5) Let's say Billy is sharp, hard-working and has the loving support
of family and friends. Does Billy have a fighting chance to have any
real impact at his alma mater to change how things are done? Consider
the cases in questions 3 and 4: one where he is in the right, and the
other where he wants to change the law or how the law is interpreted.
Broadly speaking, how effective could a "one-man show" be against a
powerful institution with wide network of support in an area?
Billy could form a 'Let Billy show up to every meeting' party, run candidates for the legislature in every State and federally, lobby hard, raise funds for lawyers to run test cases, change the constitution, take control of the armed forces, pass a resolution through the United Nations General Assembly, etc etc. Watch the look on those university bureaucrats' faces when Billy arrives to their next staff meeting aboard Air Force One and flanked by the Russian special forces, a Chinese aircraft carrier and an elephant.
Or maybe people decide they want university officials to be able to talk to each other without Billy present sometimes, so they pass a statute codifying the officials' administrative practice to have the force of law, to foreclose judicial review. Who knows? Maybe the campus police will just beat Billy up every day until he gets a new hobby.
