I'm not sure you understand the concept. It's never been seriously suggested that the right to keep and bear arms implies that the government must supply a gun for me. The right to habeas corpus doesn't say that the government has to do anything to make me comfortable, just that I retain ownership of my person. Equal protection doesn't say anything about equal outcomes, just that the law must not view any of us differently.
There really is a fundamental difference in saying that the government must not do something (the negative rights angle), versus that the government provide us something (the positive rights angle).
To me this is a total no-brainer: the answer is obviously yes, notwithstanding that the Constitution does not explicitly say so. I don't see any point in quibbling over what flavor of right this is.
In terms of a contract or in modern welfare state entitlements (such as Social Security), "rights" indeed refer to benefits owed. Kimmel wasn't referring to the Federalist Papers when he made his speech; it was an informal humanitarian modern-welfare-state understanding of "rights".
I agree that there should probably be some limit to the amount an insurance company needs to fulfill claims, otherwise our premiums are likewise unbounded. The NHS and Canadian health systems appear to have rate limiting aspects (perhaps unintended) that have the outcome of bounding costs.
That depends very much on your interpretation. Habeus corpus. The right to bear arms. The right to confront witnesses against you. Trial by jury. Equal protection. All those seem like "positive rights" to me.
Furthermore, it seems to me that you are doing exactly what the 9th amendment prohibits: you are extrapolating from the enumerated rights to make inferences about non-enumerated rights, and to conclude that because all of the enumerated rights fit some pattern that you discern, all of the non-enumerated rights must fit the same pattern, and so you can deny and disparage those non-enumerated rights that don't fit your perceived pattern.
Well, no. The 9th amendment was specifically intended to prohibit this kind of reasoning. Some of the framers didn't want a Bill of Rights at all because they were afraid (and apparently rightly so) that people would mount exactly the kind of argument that you are mounting.