In many cases, charter schools are both publicly funded and administer. The charter is a governing document providing exceptions and alternatives to the governing rules otherwise applicable to public schools.

Charter schools may be privately operated/administered, but that's not universally the case.

Yes they do. You always have a choice of charter school or non-charter school. Many charters are so popular that they have 10 applicants for every spot. This isn't the sign of a lack of a voice, it's a sign of people voicing their displeasure with their terrible zoned schools.

We allow airlines to compete for our business, and the bad ones should close. We allow grocery stores to compete for our business, and the bad ones should close. Why not allow schools to compete for business and let them close?

Charters have more accountability than district public schools. If a charter misses it's #s, it won't get renewed. Every 5 years they have to prove themselves.