Usual questions would be:
How many in each class (although KS1 will be max 30 by law).
Do they teach in mixed classes at all eg. R/Y1 or Y1/2 or Y5/6.
How are these mixes selected? Ability or age. How does this affect your child based on when they born.
What sports do they play? Does everyone get a turn in any school teams or are they selected by ability.
Are their opportunities to learn musical instruments within school and at what age? Are these at additional cost?
Are there opportunities to take part in school plays? Is it compulsory or by choice/
Where do the majority of pupils go after year 6? Which secondaries?
I assume you'd have looked at Ofsted reports and SATS results but if there was anything "odd" query this. Eg. if SATS suddenly dipped last year. Was it a cohort problem? Had they lost staff?
What is staff turnover like?
Do you get a good feel about the place and the pupils?
How are the pupils behaved and presented?
What is the uniform code and is it strictly adhered to? If you don't agree with it and are going to break the rules then consider going somewhere where it is more lax.