That's probably just called homeschooling. The way I described how my parents' homeschooled me in highschool is that they were a general contractor for my education. Writing classes were online, history classes were from the local community college, other activities from the co-op, calculus was from a textbook supervised from my engineer dad, etc.
I don't think so. My wife was 'homeschooled'. Her mother didn't like some of her classes in public school so pulled her out of them, such that she wasn't spending the required amount of time in the public school. Thus, my mother registered her as a homeschooler, so my wife didn't need to be in the classroom.
Of course, the public schools here have to take your child if you drop them off.
My wife is well-socialized, extremely well-educated, and way better off than her peers, so it worked.
This blog I wrote about how to start a microschool /learning pod/hybrid school might be helpful to you . Please let me know if you’ve got any specific questions I can be of support with
It depends on your state and the ages of the children involved. Sometimes it can get more tricky if kids are younger than five because that triggers DOH laws as well as DOE laws.
E.g. is it possible for me and a few other neighborhood families hire a private tutor for our kids?