An individual can sign up for a plan through their State’s health insurance exchange or the federal government’s HealthCare.gov website.
It is usually more expensive than getting it through an employer - but works to serve small business owners, freelancers, etc.
A few States (like Massachusetts) have semi-universal systems that cover all individuals that earn under 150% of poverty, independent students, newly unemployed, etc.
A lot of Americans are also covered under Medicare, Medicaid , Social Security and other programs.
Retirees aged 65 and older are eligible for Medicare - a semi-universal federal system that covers pretty much everything and accepted most places.
A university is a typically a collection of colleges (or schools).
For example: Harvard University is made up of Harvard College, Harvard Business School, Harvard Divinity School, Harvard Kennedy School, Harvard Law School, Paulson School of Engineering and Applied Sciences, etc.
For all intents and purposes - we use the word “college” and “university” interchangeably because they’re the same level of education. Either can do associates through doctoral.
Community colleges, however, only focus on 2 year degrees and certain certifications.