Other possible questions:
How is pupil progress tracked throughout the year and across the year groups ie vertically and horizontally (eg just through SATS or anything else)?
How is diversity of ability dealt with in the class room, at both ends of the spectrum (eg through sets or otherwise).
Is IT taught as a specific/discrete subject or through other subjects?
What kind of focus is there on life skills?
How is REligious Education taught if at all?
What kind of incentives/rewards and disciplne systems are in place.
Number of children per class and teacher/pupil ratio?
Governing Board, what is its composition (the Board is responsible for appointment of the Head and strategic direction of the school).
You should be able to ask for or obtain copies of school policies eg bullying, IT, child protection and results ie where do the children go after year 6 or if secondary, what their GCSE and A levels/IB results are.
Would also ask about curriculum and whether English or IB (international Baccalaureate), probably more relevant for secondary, most schools follow English National Curriculum in the UK but some Independent schools seem to be going down the IB road these days too.
Agree with suggestion to look up Ofsted/Inspection reports for all schools and find out how regularly the school is inspected and when it is due it's next inspection.
Good luck and hope you find somewhere you are happy with, also agree ambiance can make a lot of difference ie the feel of the place.