2) Customs was a power given to the federal government, as it was the primary method of taxation, and regulation of international commerce.
3) The ratifiers of the Constitution were most concerned with preventing general warrants, as had been commonly issued by the British as a tool of invasive monitoring and oppression, and the Fourth Amendment was included to prevent these practices. The warrant-less searches we see today are operating in a manner similar to the general warrants, but without even an explicit general warrant.
4) The Constitution has no provision allowing for Congress to delegate any criminal, civil, or regulatory law or rule-making, thus such delegation is un-enumerated and impermissible. The president only has the authority to "take Care that the Laws be faithfully executed", and not even to exercise discretion in an arbitrary fashion.
5) The Tenth Amendment is simply an explicit statement that all powers not explicitly mentioned in Article I, Section 8 are out-of-bounds for the federal government.
2) Nothing in the Constitution gives the federal government power over "customs." It gives Congress the power to "collect duties." Clearly, Congress interpreted that in 1789 to mean it could create an agency to administer the collection of duties. But that same reasoning applies to any other agency, when the subject of that agency's duties involves an enumerated power.
3) General warrants gave authorities the right to go into peoples' houses and search them for contraband with no probable cause. Warrantless searches we see today do not allow the government to do that. Also: the Constitution doesn't say anything about general warrants. It just prohibits "unreasonable searches." What is there in the text of the Constitution to say that an warrantless exigent circumstances search or a border search is "unreasonable?" Besides your own opinion?
4) The Constitution "vests" legislative powers in Congress. The non-delegation doctrine interprets "vests" to require Congress to exercise those powers itself, but nothing about the words requires that construction. E.g. Article I gives Congress the power to "collect taxes." Obviously Congress can delegate that authority--the Constitution clearly does not contemplate Congress itself going out and collecting taxes.
5) No, the 10th amendment says "the powers not delegated to the United States by the Constitution" are out of bounds for the federal government. But the 10th amendment isn't what makes that true--it's inherent in the design of the Constitution. So any 10th amendment issue is really a fight about what was "delegated to the United States by the Constitution."
2) I agree that Congress created the Customs Service to carry out an enumerated power according to laws passed by Congress, and would say that the Navy, Internal Revenue Service, and Treasury were created in a manner compliant with the constitution (and its amendments). Health and Human Services, Housing and Urban Development, and the Department of Education are not compliant with the Constitution.
3) I agree that searches of foreigners at the border are not even required to be reasonable, and searches of citizens must only be reasonable. Reading people's correspondence without a warrant was never considered 'reasonable', and I have no evidence that 'metadata' was considered less important than the contents of the correspondence. There is also no provision for 'collecting and storing information about citizens, but not looking at it unless you really want to'.
4) According to my reading of the Constitution, Congress must establish the laws/rules for the collection of revenue, and fund/authorize the relevant agency. After Congress does this, it is the President's job to "take care that the laws be faithfully executed", which I interpret as meaning that they should hire and supervise people to do the job Congress told them to do.
5) I sympathize with your view, but the entire Bill of Rights was meant to be a dead-letter by that definition. I am sure you aware that some founders made the case that the Bill of Rights was entirely superfluous, as the federal government had never been given the power to regulate speech or firearms, search citizens arbitrarily and invasively, force them to confess to crimes, or forcibly station soldiers in their homes. Unfortunately, the Bill of Rights has proven to be vital (if insufficient) to the preservation of liberty.
Regarding (5): The framers in fact rejected a previous iteration of the language of the 10th Amendment that would have reserved to the states any powers not expressly delegated in the Constitution. So we know that's not what they meant.
Yes, I agree that the states were not delegated all powers not expressly delegated by the constitution, but "the people and the states" were. I have never heard a better explanation for the 10th amendment than to say that it was restating the enumerated powers doctrine (though I cannot recall where I first heard that explanation). If you have a better explanation of the 10th amendment, I am very interested to learn what it is.
Regarding your second point: the change was not "states" vs. "people and the states". The change was whether the rights referred to were solely those expressed in the Constitution, or something broader. Broader won. This is an argument you are going to need to take up with the authors of the Constitution, because they do not agree with you.
On the one side you have the "But the Framers didn't have machine-guns, or CRISPR." On the other side you have people who would ask "So I don't actually have a right to use strong encryption? I don't have a right to build a rocket? I don't have any rights that were not imagined by the Framers? All new inventions have to be allowed before they can be used?"
Otherwise anything could be "necessary and proper."
So, let's have a hypothetical about something really fundamental: If I could CRISPRize negligible senescence, or superintelligence, do I have the right to do it?
Do you have the right to use strong encryption? If you can fit it into a right the framers would have recognized based on English law and tradition (probably free speech), then yes. If not, then no. The 10th amendment has nothing to say about that.
Fundamentally, the Constitution is not really about "rights." The Bill of Rights was added to appease those who were worried the central government would impinge on the traditional rights of Englishmen. But the real purpose of the exercise was to create a powerful, but democratic, central government that had the authority to do the things that needed to be done.
To be precise, the 10th amendment is a nullity if you already accept that the federal government is one of enumerated powers. At the time of the founding, that was a novel concept and it probably made some people feel better to have it stated explicitly. But today that's taken as a given. The debate is never over if the government has powers not enumerated, but whether a particular action falls within the scope of an enumerated power. And the 10th amendment tells you nothing about the scope of the enumerated powers.
1) The federal government is one of enumerated powers, but it has plenary authority over areas it is allowed to regulate. The Constitution gave the federal government the power to tax, spend, and "regulate interstate commerce." In a world where interstate commerce is pervasive, giving the federal government those powers allows it to do almost pretty much everything. But those are the words on the page! Just because the result might have surprised framers who were thinking about independent agrarian farmers for whom an interstate transaction might be the rare exception does not mean you can ignore what the words on the page mean.
2) As to agencies, the Constitution creates an executive, and contemplates the existence of executive deparments. The first agency, the customs service, was created by the first Congress in 1789!
3) The Constitution prohibits only "unreasonable" searches and seizures. That implies the power to search and seize. And the idea that warrentless searches are presumptively unreasonable is as much a judicial-created gloss on the Constitution as the idea of exceptions to the warrant requirement. Remember: the very first Congress created a scheme of warrantless searches by the Customs Service.
4) The non-delegation principle is itself a judicially-created concept. It's not in the Constitution.
5) The 10th amendment never meant anything. It literally says "any power not granted to the federal government is reserved to the states or to the people." It doesn't provide any basis for deciding what those powers are. Take something like Obamacare. If that's a legitimate exercise of of the taxing or commerce power, it by definition cannot violate the 10th amendment because it's an exercise of an enumerated power. And if it wasn't a valid exercise of those powers, it's void for not being a valid exercise of an enumerated power. The 10th amendment can never be the reason a law is invalid.