Though not explicitly mentioned by the U.S. constitution, the right to education has been recognized by several major international conventions, many of which the U.S. is regular participant. The U.S. also signed the Universal Declaration of Human Rights, of which right to education is an article. You can say that this is not legally-binding, but to think that the U.S. government is interested in denying any citizen of education would be mistaken, as this protection is routinely upheld by supreme courts around the country.
Again, legally speaking, you are correct. Its not a "right." However, I believe that it should be (along with education) as its just common sense if you care at all about the prosperity of your nation. You can disagree with my previously stated rationale as to why I think it should be a right, and we can agree to disagree.
This is just nonsense. First of all, the president doesn't have that kind of power. Second of all, when did Bernie say he wants to "do away" with ALL private insurance, virtually or otherwise? Third of all, to think that Bernie's vision of universal healthcare will come to full fruition is naive. Of course it would ultimately be just some watered-down compromise where the jobs of those possessing the most well-funded health insurance and hospital corporation lobbyists will remain protected, and likely Bernie won't even affect any real change in the industry, similar to what happened with Obama.
However, its still a step in the right direction - that we're at least willing to look at solutions to a massive problem - as the current healthcare system is heavily flawed and entirely unsustainable.