K-12 are "free" (funded in large part by property taxes, as I understand it). Higher Education is not, though public colleges tend to be cheaper, from what I've seen.

That would be nice, wouldn't it?

US community (2-year) colleges tend to be very affordable.

US public universities may have lower fees for in-state students. UC Berkeley costs some $46K per year for CA residents - not particularly affordable to begin with - but charges an extortionate $33K "nonresident tuition fee" on top of that for non-resident students (including students under 24 with non-resident parents/guardians.)

Public in what sense? Elementary through Secondary aka K-12 is, but is mandatory for students unless they take extra-ordinary measures to not be there, e.g. homeschooling, or dropping out at 16. Funding through this is usually handled on the state and local level, often by local property taxes.

Public Universities are ones funded by the state, to varying degrees.

Private Unis have their own funding, usually through a mix of tuition and large endowments.