There's not an explicit minimum speed limit, but note that the officer didn't say you were below the limit - he said you obstructed traffic. The limit on that highway is probably about 70 mph, and in the picture it's a single lane with double lines. If any cars need to use the highway while you bike, they will very quickly end up stuck behind you driving at ~20 mph (if that) with no way of legally passing you. So you really would be obstructing traffic.
This isn't specific to bikes - a car driving 20 mph would come under the same rule. Even if the car was driving that slow due to damage, it might still be considered obstruction because the driver didn't choose a slower road. Even if the damage was caused on the road, the officer might tell you to get a tow truck instead. Of course in the realistic situation of getting a flat tire and having to drive 40 on your spare they would probably be more understanding.
Generally the solution to such situations is that the slow vehicle pulls right into the shoulder (and maybe even stops), letting the faster traffic go around. It is technically an illegal pass (not if you pull over and stop) but rarely punished. Possibly you could have also biked on the shoulder or the grass. In any case, when a cop does tell you to stop doing something, your best option is to comply (as you've found out). Keep in mind that riding bikes on a highway is not a constitutional right.
The arrest and ensuing court case was clearly not caused solely by biking, but also refusing to show ID as well as the Tylenol. In all, it doesn't sound very fair, but it's one of those grey areas where you technically didn't do anything illegal, but did get clever with the cop/system, and as a result the system exercised its bureaucratic power to give you the run around. Again, I don't see how your constitutional rights are violated here - if you do, feel free to go to the Supreme Court (and I'd be happy for you if you did - as I said, the situation is unfair and I wish it didn't happen). Unfortunately, the founding fathers did not have the wisdom to include freedom from bureaucracy in the bill of rights. The right to speedy and fair trial is unfortunately subject to reinterpretation of what exactly counts as speedy or fair, just as many other parts of the constitution. In any case, this slow creep of judicial activism is not something you can fight by annoying cops, you can only fight it by voting and possibly practicing in the Supreme Court. I say possibly because I'm skeptical that any legal professional ultimately has much power over the Supreme Justices.
Alternatively, you can also try to sway public opinion so that the police departments change policy, which has actually been happening for bike related law over the past years, but that is not very related to your objections on constitutional grounds.
Is making up a law on the spot an acceptable alternative to the requirement that the cops have to have a reasonable suspicion in order to detain a civilian?
In theory, no. In practice, this is pretty common in the US. Police often don't know the law or they are wrong about it. Whether it is still a reasonable suspicion if the cop misunderstood the law is for the court to decide - and in cases such as yours where there is injustice but not gross injustice and no significant political issue is served by siding with you, the courts tend to default to siding with the police. Also the courts really don't like people making light of the court's rules, so if you flout them, they can "make an example" by throwing the book at you just to ensure that nobody else gets funny ideas in the future.
Remember, "Injustice anywhere is a threat to justice everywhere"
Injustice is indeed bad, but in your last election, did anyone run on a platform eliminating injustice (legal, not economic or social) and upholding constitutional rights? Did you vote for them? Did they win? Did they do what they promised? If not, then as an ideal it is nice, but not very useful to understanding the legal reality.
Was the cop right? Does anyone know of a "minimum speed limit" on US hwy 60 ?
Right to stop you? I'd say yes, based on the first part of my answer. Right to arrest you? Per se, no, it seems unnecessarily heavy-handed. But then you did provoke him by disobeying. I still don't think needlessly harsh treatment from police is justified just because you annoyed the cop, but realistically, you can't expect to annoy a person with power and have no repercussions. You could claim you were harassed, but you wouldn't have a case because the harassment was very minor and debatable.
Was the judge right to make me come back to OK (under threat of arrest warrant) just to tell me that he can not dismiss the case (in case I was to plead not guilty) ?
It's certainly mean of him to do that, but then he doesn't owe it to you to be nice. As for legally, he is perfectly within his rights. Missouri isn't that far and expecting you to appear in court for the arrest is not unreasonable. Granted, for such a trivial thing it's a bit unnecessary - which is why if you are cooperative the police will often offer you the opportunity to "just pay the fine and make it go away". But then we come back to the issue of your attitude to the officer.
I'm not saying that you're not in the right here, but you have to consider that cops are not robots but human beings, as are the courts. Even if it is illegal for him to arrest you, he might arrest you anyway if you give him a reason (such as annoying him). Yes, legally you could then seek restitution and punishment for the cop. But you will have to convince the court of your case, in which you may or may not succeed. Either way, it can cost you money and time. So you have to think of the law not as a law of nature, but as a guideline that will probably be followed more or less, and eventually the courts will ensure some measure of justice (although justice according to them, not you, and based on what they think the situation was, and not reality). But in terms of the here and now, you have to also consider the human factor, which might dominate over the legal in determining what will happen next and whether you'll be happy with it.
This is a screenshot of US hwy 60 (Limestone). It is clearly not a "controlled access highway"
