Too poor to obey the law It's illegal to walk around naked in public, but what if someone is literally too poor to afford clothes?
This situation is unlikely to come about in practice. If you were born into such extreme poverty, your parents would considered guilty of child neglect, and CPS/social services would take you into foster services where you would be given clothes. If you previously had clothes, but recently became poor, it is very unlikely that any creditors would repossess your last shirt off your back. It would probably be illegal for them to leave you in that situation, and a used shirt wouldn't be worth much. For the same reason, it's unlikely you would sell your last shirt to, eg. pay for food: Who would buy it? For how much? In many countries, there are extensive welfare systems and private charities that private food, free clothing and other resources to the very poor. Even before you lost your last clothes, you could go to these for assistance. So again you are unlikely to involuntarily end up in this position. Also, technically the amount of clothes you are required to wear is usually very small. I believe you are usually only required to cover the groin and breasts if female. In theory you could easily collect a discarded plastic bag, piece of paper, scrap fabric, cardboard box or some other trash to fashion a crude loincloth. Lastly, when the police do show up and arrest you, you will likely have the opportunity to explain to them your situation. They would probably try to get you some basic clothing and other assistance. But if they do end up pressing charges, you would be able to either convince the judge to let you off or challenge the law itself for failing to consider poor people like you. Generally, laws are designed such that there is always an option to follow them and nobody would be "too poor" to comply, failing to do this could make a politician extremely unpopular. Many laws with significant cost burden offer alternatives to the poor. Courts will also tend to be sympathetic to cases such as this. But as I said, the situation is very unlikely to come about.
In the case of the US, the only anti-discrimination laws that would cover an event is the Civil Rights Act of 1964, under the rubric "public accommodation", in Title II. But that law does not prohibit sex discrimination. The extent of "public accommodation" is not clearly defined, but generally is held to be about "a place", and would include "entrance into this facility". It might be illegal in California, though, since the Unruh Civil Rights Act is more generic, not excluding sex on this point. The main issue would be whether this organization is a "business".
Legally there is no problem. What you say is protected speech under the 1st Amendment as long as it is either true or a matter of opinion. However Ron Beyer's comment is a good one; while legal this sounds very inadvisable. You would be far better off hiring a lawyer. The Mr Dicks of this world make money from the widespread fear of legal action. He will probably fold as soon as he sees a letter from a lawyer threatening a lawsuit. Until then stalling doesn't cost him anything so he will carry on doing it. BTW, don't delay. I don't know about the US, but over here in the UK there are a number of ways that people like Mr Dick can make it hard to collect. Don't give him time to play shell games with his assets.
Yes, of course. Anyone can walk up to a shop owner and ask them pretty much whatever questions they want; police have just as much of a right to do that as anyone else. The shop owner doesn't have to answer, but police are free to ask.
Sometimes running away is a juvenile offense, but it is not an offense for which an adult aged eighteen or over would be arrested or punished. An adult would not be returned home.
Let's say you leave fake drugs in someone's yard. Eg, you expect the police to be dumb enough to believe it and arrest the other person Obstructing a public officer, specifically "deliberately hindering a public officer from carrying out official duties". Trespassing.
An existing law actually prohibits using census data "against" a person, see this recent question. The 5th Amendment ("nor shall be compelled in any criminal case to be a witness against himself") is not interpreted to imply an absolute privilege to not answer, it means that your answer cannot be used against you in a criminal case. You can be compelled to testify "against yourself" if you are granted immunity from prosecution.
If I want to protest for or against President Trump and decide to wear a Trump mask, isn't that speech protected by the first amendment? Probably. The matter of intent, in any event, is for a court to decide (if the prosecutor determines that the question should even be presented to a court). For example, someone seeking to rob a bank in a mask would probably fall afoul of this law, and it's not likely that using a mask of a political figure would enable a successful first-amendment defense. For a political protestor, it could be easy to show that the intent was to make a political statement and not to conceal identity, in which case it would not be necessary to consider the constitutional question, for a critical element of the crime would be missing. That is, if you say "I wasn't trying to hide my identity," and the court believes you, then you haven't violated the statute. That is a separate question from whether the statute is constitutional. For the law itself to be unconstitutional, it would have to be unconstitutional in every application, generally. If some applications of the law are unconstitutional, the law could stand, but prosecutions for the unconstitutional application would not succeed.