Short Answer: None.
So if the Constitution doesn't grant those things to citizens, how can we remove them from non-citizens?
It's blatant historical revisionism to assert that a group of people who didn't believe that black people in America had any rights somehow believed in a concept of universal natural rights that we should apply to people in Yemen or Afghanistan.
The Constitution is fundamentally a product of "social contract" thinking. The preamble says:
"We the people of the United States, in order to form a more perfect union, establish justice, insure domestic tranquility, provide for the common defense, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity, do ordain and establish this Constitution for the United States of America."
When you see uses of "the people" in say the First Amendment, it's a clear reference to "the people of the United States" not "people everywhere." It's not necessarily limited to U.S. Citizens, but it is limited to people who have some nexus to the U.S., either through citizenship or presence on American soil.
Clearly there are laws, and the US government is bound to those laws. Are you saying that the US government can have people killed? Torture? And as long as the US legal system isn't there to intervene it is legal?
It's not a matter of patriotism, it's a matter of self-preservation. We acknowledge that other people in our own society have rights because we also understand that they have reciprocal obligations. If there is conflict, we can resort to legal process to mediate the conflict and preserve everyone's rights. This is possible because we are all party to the same social contract.
But people outside our society do not have any obligation to us. They are not party to our social contract. We in America cannot legislate how say the Chinese go about their business, even when those activities might have an impact on us (e.g. air pollution in California). That is why we don't acknowledge that they have rights identical with those of people in our own society.