Every nursery will have different policies. So there is no such thing as "normal".
Some have to follow the 'healthy schools commitment'. So parents can only bring in 'healthy snacks' i.e fruit, rice cakes etc... We had to switch to this after the parties got competitive- cakes, sweets & crisps & party bags + with other parents not being able to afford anything.
So we said no to all cakes, but let the children plan a party where they got to choose the music & activities.
Some don't mind what you bring- as long as it is store bought, ingredients listed, & no nuts.
Others will have children who have real issues with various allergies so will have to give you specifics.