WW schooling and British schooling

[Melody]

No: HPFGUIDX 44000

I was wondering something and I was hoping ya'll could help me.

Do Hogwarts students pay tuition?
And if not, then how can Hogwarts afford to stay running?
Do you think the Wizard world is taxed?
Do these taxes pay for more than just the school system?
Is Hogwarts then a state school?

I am not sure if this is just a cultural misunderstanding (between 
British and American ideas) or questions that are viable.  

Any thoughts?

Melody