Not every right is absolute; some rights may be constrained, some rights are both a right and a responsibility. Not every right is a responsibility.
Almost. Every right IS absolute, but with limits, if your rights harm innocents they are still rights, however, the actions have consequences, legal consequences for the aggressor, and practical for the victim, thus the protections of those rights dissappear because of those abuses of the rights, rights do carry responsibilities......however these responsibilities aren't mandates, they are simply consequences due to misuse.
There is a question about whether a mandate for health insurance is constitutional
It isn't.
For the record, I believe a mandate is probably constitutional.
No, first, healthcare is a service, as is healthcare coverage. There is no right to healthcare because of this fact, it would take a very large logical leap to suggest otherwise, however, even IF healthcare could be proven a right, the extension of said right ends at ability to provide on the individual, which is the responsibility of the individual. Finally, if one cannot be forced to assemble, own a gun, join a religion, own a house, etc., then they cannot be forced to participate in healthcare policy if it is a right, only if it is a government mandated(which would be unconstitutional on the federal level as it is beyond it's scope of power) program could the argument be made for a healthcare requirement.