Even in states that do not regulate the coursework of home school grads it is worth considering how that diploma will be view by colleges. If colleges expect to see a certain number of credits in various subjects a transcript that doesn't have some similarity to what they expect might not get a second look.
Yep, it's in the property tax and sometimes it's a separate school tax (it is here). Even if you pay rent, that's public knowledge so you can find that out.