1. Require private schools to sponsor at least one academy, and/or work in partnership with an academy provider, giving access to facilities and staff.
A lot depends on size and type of school of school. Prehaps very small private schools should team up so that they are not bancrupted. Also some private schools are such poor quality they have nothing to offer the state sector in expertise. I really don't want some weird fundermental christian private school sponsoring my daughter's failing school.
2. Allow private schools to convert to state school status through the Free Schools & Academies Programme.
That is already the case.
3. Make private school charitable status conditional on freely offering 25% of places via random lottery to the most vulnerable children. No academic selection allowed.
Unworkable. This would push the fees up so high as to bankcrupt the school.
4. Weaken the link between private schools and top universities by providing the highest GCSE scorer in each state school the opportunity to take a guaranteed interview at their choice of Cambridge, Durham or Oxford.
Unworkable
5. Disclosure of private schools’ accounts to give full details of bursaries, charitable activities and their impact.
Happens already
6. Agree to take part in a Cross-Party Commission dedicated to finding the most practical way to fully implement these policies.
Assuming that there would be any cross part, yet a lone private school for some of these looney policies. Private schools already have considerable influence on goverment policy.
I get the feeling the OP is anti private schools